Irena Penev
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Research Interests
Irena Penev has a total of 20 co-authors. Here are the top co-authors by number of shared publications:
- Kristina Vušković
School of Computing, University of Leeds, Leeds LS2 9JT, United Kingdom
6 shared publications - Martin Milanič
University of Primorska
3 shared publications - Ana Laura Trujillo-Negrete
Instituto de Matematicas Universidad Nacional Autónoma de México Mexico City Mexico
2 shared publications Frédéric Maffray
CNRS, Laboratoire G‐SCOP Université Grenoble‐Alpes Grenoble France
2 shared publicationsS Taruni
Centro de Modelamiento Matemático (CNRS IRL2807) Universidad de Chile Santiago Chile
2 shared publications- Shenwei Huang
School of Mathematical Sciences and LPMC Nankai University 300071 Tianjin P.R. China
2 shared publications
Latest Publications
- Open Access
- 9 September 2026
- Published by Wiley in Journal of Graph Theory
Two‐Block Paths in Oriented Graphs of Large Semidegree
We study the existence of oriented paths with two blocks in oriented graphs under semidegree conditions. A block of an oriented path is a maximal directed subpath. Given positive integers and with , we establish a semidegree function that guarantees the containment of every oriented path with two blocks of sizes and . As a corollary, we show that every oriented graph with all in‐ and out‐degrees at least contains every two‐block path with arcs. Our results extend previous work on Stein's conjecture and related problems concerning oriented paths.
- 9 September 2026
- Published by Wiley in Journal of Graph Theory
Open AccessTwo‐Block Paths in Oriented Graphs of Large Semidegree
We study the existence of oriented paths with two blocks in oriented graphs under semidegree conditions. A block of an oriented path is a maximal directed subpath. Given positive integers and with , we establish a semidegree function that guarantees the containment of every oriented path with two blocks of sizes and . As a corollary, we show that every oriented graph with all in‐ and out‐degrees at least contains every two‐block path with arcs. Our results extend previous work on Stein's conjecture and related problems concerning oriented paths.
- Open Access
The class of $(2P_3,C_4,C_6)$-free graphs, part II: $(2P_3,C_4,C_6,C_7,T_0)$-free graphs
This is the second in a series of two papers dealing with $(2P_3,C_4,C_6)$-free graphs, or equivalently, $(2P_3,\text{even hole})$-free graphs. In this two-paper series, we give a full structural description of $(2P_3,C_4,C_6)$-free graphs that contain no simplicial vertices, and we show that such graphs have bounded clique-width. This implies that Graph Coloring can be solved in polynomial time for $(2P_3,C_4,C_6)$-free graphs. In the first paper of the series, we described the structure of $(2P_3,C_4,C_6)$-free graphs that contain an induced $C_7$ or an induced $T_0$ (where $T_0$ is a certain 2-connected graph on nine vertices in which all holes are of length five), and we showed that such graphs either contain a simplicial vertex or have bounded clique-width. In the present paper (the second part of the series), we describe the structure of $(2P_3,C_4,C_6,C_7,T_0)$-free graphs that contain no simplicial vertices, and we show that such graphs have bounded clique-width. Finally this paper gives the full statement of the theorem describing the structure of $(2P_3,C_4,C_6)$-free graphs that contain no simplicial vertices.Open AccessThe class of $(2P_3,C_4,C_6)$-free graphs, part II: $(2P_3,C_4,C_6,C_7,T_0)$-free graphs
This is the second in a series of two papers dealing with $(2P_3,C_4,C_6)$-free graphs, or equivalently, $(2P_3,\text{even hole})$-free graphs. In this two-paper series, we give a full structural description of $(2P_3,C_4,C_6)$-free graphs that contain no simplicial vertices, and we show that such graphs have bounded clique-width. This implies that Graph Coloring can be solved in polynomial time for $(2P_3,C_4,C_6)$-free graphs. In the first paper of the series, we described the structure of $(2P_3,C_4,C_6)$-free graphs that contain an induced $C_7$ or an induced $T_0$ (where $T_0$ is a certain 2-connected graph on nine vertices in which all holes are of length five), and we showed that such graphs either contain a simplicial vertex or have bounded clique-width. In the present paper (the second part of the series), we describe the structure of $(2P_3,C_4,C_6,C_7,T_0)$-free graphs that contain no simplicial vertices, and we show that such graphs have bounded clique-width. Finally this paper gives the full statement of the theorem describing the structure of $(2P_3,C_4,C_6)$-free graphs that contain no simplicial vertices. - Open AccessThe class of $(2P_3,C_4,C_6)$-free graphs, part I: $(2P_3,C_4,C_6)$-free graphs that contain an induced $C_7$ or an induced $T_0$This is the first in a series of two papers dealing with $(2P_3,C_4,C_6)$-free graphs, or equivalently, $(2P_3,\text{even hole})$-free graphs. In this two-paper series, we give a full structural description of $(2P_3,C_4,C_6)$-free graphs that contain no simplicial vertices, and we show that such graphs have bounded clique-width. This implies that Graph Coloring can be solved in polynomial time for $(2P_3,C_4,C_6)$-free graphs. In this paper, we describe the structure of $(2P_3,C_4,C_6)$-free graphs that contain an induced $C_7$ or an induced $T_0$ (where $T_0$ is a certain 2-connected graph on nine vertices in which all holes are of length five), and we show that such graphs either contain a simplicial vertex or have bounded clique-width. In the second part of this series, we describe the structure of all $(2P_3,C_4,C_6,C_7,T_0)$-free graphs that contain no simplicial vertices, and we show that such graphs have bounded clique-width. The full statement of the theorem describing the structure of $(2P_3,C_4,C_6)$-free graphs that contain no simplicial vertices is given in the second paper of this series.Open AccessThe class of $(2P_3,C_4,C_6)$-free graphs, part I: $(2P_3,C_4,C_6)$-free graphs that contain an induced $C_7$ or an induced $T_0$This is the first in a series of two papers dealing with $(2P_3,C_4,C_6)$-free graphs, or equivalently, $(2P_3,\text{even hole})$-free graphs. In this two-paper series, we give a full structural description of $(2P_3,C_4,C_6)$-free graphs that contain no simplicial vertices, and we show that such graphs have bounded clique-width. This implies that Graph Coloring can be solved in polynomial time for $(2P_3,C_4,C_6)$-free graphs. In this paper, we describe the structure of $(2P_3,C_4,C_6)$-free graphs that contain an induced $C_7$ or an induced $T_0$ (where $T_0$ is a certain 2-connected graph on nine vertices in which all holes are of length five), and we show that such graphs either contain a simplicial vertex or have bounded clique-width. In the second part of this series, we describe the structure of all $(2P_3,C_4,C_6,C_7,T_0)$-free graphs that contain no simplicial vertices, and we show that such graphs have bounded clique-width. The full statement of the theorem describing the structure of $(2P_3,C_4,C_6)$-free graphs that contain no simplicial vertices is given in the second paper of this series.
- Open Access
Isometric path partition: a new upper bound and a characterization of some extremal graphs
An $\textit{isometric path}$ is a shortest path between two vertices. An $\textit{isometric path partition}$ (IPP) of a graph $G$ is a set $I$ of vertex-disjoint isometric paths in $G$ that partition the vertices of $G$. The \textit{isometric path partition number} of $G$, denoted by $\text{ipp}(G)$, is the minimum cardinality of an IPP of $G$. In this article, we prove that every graph $G$ satisfies $\text{ipp}(G) \leq |V(G)| - ν(G)$, where $ν(G)$ is matching number of $G$. We further prove that a connected graph $G$ is extremal with respect to this upper bound, i.e.\ satisfies $\text{ipp}(G) = |V(G)| - ν(G)$, if and only if either (i) all blocks of $G$ are odd complete graphs, or (ii) all blocks of $G$ except one are odd complete graphs, and the unique block $B$ of $G$ that is not an odd complete graph is even and satisfy $\text{ipp}(B) = |V(B)| - ν(B)$. As corollaries of this result, we obtain a full structural characterization of all connected odd graphs that are extremal with respect to our upper bound, as well as of all extremal block graphs.Open AccessIsometric path partition: a new upper bound and a characterization of some extremal graphs
An $\textit{isometric path}$ is a shortest path between two vertices. An $\textit{isometric path partition}$ (IPP) of a graph $G$ is a set $I$ of vertex-disjoint isometric paths in $G$ that partition the vertices of $G$. The \textit{isometric path partition number} of $G$, denoted by $\text{ipp}(G)$, is the minimum cardinality of an IPP of $G$. In this article, we prove that every graph $G$ satisfies $\text{ipp}(G) \leq |V(G)| - ν(G)$, where $ν(G)$ is matching number of $G$. We further prove that a connected graph $G$ is extremal with respect to this upper bound, i.e.\ satisfies $\text{ipp}(G) = |V(G)| - ν(G)$, if and only if either (i) all blocks of $G$ are odd complete graphs, or (ii) all blocks of $G$ except one are odd complete graphs, and the unique block $B$ of $G$ that is not an odd complete graph is even and satisfy $\text{ipp}(B) = |V(B)| - ν(B)$. As corollaries of this result, we obtain a full structural characterization of all connected odd graphs that are extremal with respect to our upper bound, as well as of all extremal block graphs. - Open Access
Two-block paths in oriented graphs of large semidegree
We study the existence of oriented paths with two blocks in oriented graphs under semidegree conditions. A block of an oriented path is a maximal directed subpath. Given positive integers $k$ and $\ell$ with $k/2\le \ell < k$, we establish a semidegree function that guarantees the containment of every oriented path with two blocks of sizes $\ell$ and $k-\ell$. As a corollary, we show that every oriented graph with all in- and out-degrees at least $3k/4$ contains every two-block path with $k$ arcs. Our results extend previous work on Stein's conjecture and related problems concerning oriented paths.Open AccessTwo-block paths in oriented graphs of large semidegree
We study the existence of oriented paths with two blocks in oriented graphs under semidegree conditions. A block of an oriented path is a maximal directed subpath. Given positive integers $k$ and $\ell$ with $k/2\le \ell < k$, we establish a semidegree function that guarantees the containment of every oriented path with two blocks of sizes $\ell$ and $k-\ell$. As a corollary, we show that every oriented graph with all in- and out-degrees at least $3k/4$ contains every two-block path with $k$ arcs. Our results extend previous work on Stein's conjecture and related problems concerning oriented paths. - Open Access
- 11 April 2024
- Published by Wiley in Journal of Graph Theory
- Vol. 106 (4) , 816-842
Bisimplicial separators
A minimal separator of a graph is a set such that there exist vertices with the property that separates from in , but no proper subset of does. For an integer , we say that a minimal separator is ‐simplicial if it can be covered by cliques and denote by the class of all graphs in which each minimal separator is ‐simplicial. We show that for each , the class is closed under induced minors, and we use this to show that the Maximum Weight Stable Set problem can be solved in polynomial time for . We also give a complete list of minimal forbidden induced minors for . Next, we show that, for , every nonnull graph in has a ‐simplicial vertex, that is, a vertex whose neighborhood is a union of cliques; we deduce that the Maximum Weight Clique problem can be solved in polynomial time for graphs in . Further, we show that, for , it is NP‐hard to recognize graphs in ; the time complexity of recognizing graphs in is unknown. We also show that the Maximum Clique problem is NP‐hard for graphs in . Finally, we prove a decomposition theorem for diamond‐free graphs in (where the diamond is the graph obtained from by deleting one edge), and we use this theorem to obtain polynomial‐time algorithms for the Vertex Coloring and recognition problems for diamond‐free graphs in , and improved running times for the Maximum Weight Clique and Maximum Weight Stable Set problems for this class of graphs.
- 11 April 2024
- Published by Wiley in Journal of Graph Theory
- Vol. 106 (4) , 816-842
Open AccessBisimplicial separators
A minimal separator of a graph is a set such that there exist vertices with the property that separates from in , but no proper subset of does. For an integer , we say that a minimal separator is ‐simplicial if it can be covered by cliques and denote by the class of all graphs in which each minimal separator is ‐simplicial. We show that for each , the class is closed under induced minors, and we use this to show that the Maximum Weight Stable Set problem can be solved in polynomial time for . We also give a complete list of minimal forbidden induced minors for . Next, we show that, for , every nonnull graph in has a ‐simplicial vertex, that is, a vertex whose neighborhood is a union of cliques; we deduce that the Maximum Weight Clique problem can be solved in polynomial time for graphs in . Further, we show that, for , it is NP‐hard to recognize graphs in ; the time complexity of recognizing graphs in is unknown. We also show that the Maximum Clique problem is NP‐hard for graphs in . Finally, we prove a decomposition theorem for diamond‐free graphs in (where the diamond is the graph obtained from by deleting one edge), and we use this theorem to obtain polynomial‐time algorithms for the Vertex Coloring and recognition problems for diamond‐free graphs in , and improved running times for the Maximum Weight Clique and Maximum Weight Stable Set problems for this class of graphs.
- Open Access
Bisimplicial separators
A minimal separator of a graph $G$ is a set $S \subseteq V(G)$ such that there exist vertices $a,b \in V(G) \setminus S$ with the property that $S$ separates $a$ from $b$ in $G$, but no proper subset of $S$ does. For an integer $k\ge 0$, we say that a minimal separator is $k$-simplicial if it can be covered by $k$ cliques and denote by $\mathcal{G}_k$ the class of all graphs in which each minimal separator is $k$-simplicial. We show that for each $k \geq 0$, the class $\mathcal{G}_k$ is closed under induced minors, and we use this to show that the Maximum Weight Stable Set problem can be solved in polynomial time for $\mathcal{G}_k$. We also give a complete list of minimal forbidden induced minors for $\mathcal{G}_2$. Next, we show that, for $k \geq 1$, every nonnull graph in $\mathcal{G}_k$ has a $k$-simplicial vertex, i.e., a vertex whose neighborhood is a union of $k$ cliques; we deduce that the Maximum Weight Clique problem can be solved in polynomial time for graphs in $\mathcal{G}_2$. Further, we show that, for $k \geq 3$, it is NP-hard to recognize graphs in $\mathcal{G}_k$; the time complexity of recognizing graphs in $\mathcal{G}_2$ is unknown. We also show that the Maximum Clique problem is NP-hard for graphs in $\mathcal{G}_3$. Finally, we prove a decomposition theorem for diamond-free graphs in $\mathcal{G}_2$ (where the diamond is the graph obtained from $K_4$ by deleting one edge), and we use this theorem to obtain polynomial-time algorithms for the Vertex Coloring and recognition problems for diamond-free graphs in $\mathcal{G}_2$, and improved running times for the Maximum Weight Clique and Maximum Weight Stable Set problems for this class of graphs.Open AccessBisimplicial separators
A minimal separator of a graph $G$ is a set $S \subseteq V(G)$ such that there exist vertices $a,b \in V(G) \setminus S$ with the property that $S$ separates $a$ from $b$ in $G$, but no proper subset of $S$ does. For an integer $k\ge 0$, we say that a minimal separator is $k$-simplicial if it can be covered by $k$ cliques and denote by $\mathcal{G}_k$ the class of all graphs in which each minimal separator is $k$-simplicial. We show that for each $k \geq 0$, the class $\mathcal{G}_k$ is closed under induced minors, and we use this to show that the Maximum Weight Stable Set problem can be solved in polynomial time for $\mathcal{G}_k$. We also give a complete list of minimal forbidden induced minors for $\mathcal{G}_2$. Next, we show that, for $k \geq 1$, every nonnull graph in $\mathcal{G}_k$ has a $k$-simplicial vertex, i.e., a vertex whose neighborhood is a union of $k$ cliques; we deduce that the Maximum Weight Clique problem can be solved in polynomial time for graphs in $\mathcal{G}_2$. Further, we show that, for $k \geq 3$, it is NP-hard to recognize graphs in $\mathcal{G}_k$; the time complexity of recognizing graphs in $\mathcal{G}_2$ is unknown. We also show that the Maximum Clique problem is NP-hard for graphs in $\mathcal{G}_3$. Finally, we prove a decomposition theorem for diamond-free graphs in $\mathcal{G}_2$ (where the diamond is the graph obtained from $K_4$ by deleting one edge), and we use this theorem to obtain polynomial-time algorithms for the Vertex Coloring and recognition problems for diamond-free graphs in $\mathcal{G}_2$, and improved running times for the Maximum Weight Clique and Maximum Weight Stable Set problems for this class of graphs. - 26 October 2022
- Published by Elsevier in Discrete Mathematics
- Vol. 346 (11)
Coloring (4K1,C4,C6)-free graphs
- 26 October 2022
- Published by Elsevier in Discrete Mathematics
- Vol. 346 (11)
Coloring (4K1,C4,C6)-free graphs
- 30 September 2021
- Published by Wiley in Journal of Graph Theory
- Vol. 99 (3) , 435-460
On the structure and clique‐width of (4K1,C4,C6,C7)‐free graphs
We give a complete structural description of -free graphs that do not contain a simplicial vertex, and we prove that such graphs have bounded clique-width. Together with the results of Foley et al., this implies that -free graphs that do not contain a simplicial vertex have bounded clique-width. Consequently, Graph Coloring can be solved in polynomial time for -free graphs, that is, for even-hole-free graphs of stability number at most three.- 30 September 2021
- Published by Wiley in Journal of Graph Theory
- Vol. 99 (3) , 435-460
On the structure and clique‐width of (4K1,C4,C6,C7)‐free graphs
We give a complete structural description of -free graphs that do not contain a simplicial vertex, and we prove that such graphs have bounded clique-width. Together with the results of Foley et al., this implies that -free graphs that do not contain a simplicial vertex have bounded clique-width. Consequently, Graph Coloring can be solved in polynomial time for -free graphs, that is, for even-hole-free graphs of stability number at most three.- 28 October 2020
- Published by Wiley in Journal of Graph Theory
- Vol. 96 (4) , 642-683
Coloring rings
A ring is a graph whose vertex set can be partitioned into nonempty sets, , such that for all , the set can be ordered as so that . A hyperhole is a ring such that for all , is complete to . In this paper, we prove that the chromatic number of a ring is equal to the maximum chromatic number of a hyperhole in . Using this result, we give a polynomial‐time coloring algorithm for rings. Rings formed one of the basic classes in a decomposition theorem for a class of graphs studied by Boncompagni et al [J. Graph Theory 91 (2019), 192–246.]. Using our coloring algorithm for rings, we show that graphs in this larger class can also be colored in polynomial time. Furthermore, we find the optimal ‐bounding function for this larger class of graphs, and we also verify Hadwiger's conjecture for it.
- 28 October 2020
- Published by Wiley in Journal of Graph Theory
- Vol. 96 (4) , 642-683
Coloring rings
A ring is a graph whose vertex set can be partitioned into nonempty sets, , such that for all , the set can be ordered as so that . A hyperhole is a ring such that for all , is complete to . In this paper, we prove that the chromatic number of a ring is equal to the maximum chromatic number of a hyperhole in . Using this result, we give a polynomial‐time coloring algorithm for rings. Rings formed one of the basic classes in a decomposition theorem for a class of graphs studied by Boncompagni et al [J. Graph Theory 91 (2019), 192–246.]. Using our coloring algorithm for rings, we show that graphs in this larger class can also be colored in polynomial time. Furthermore, we find the optimal ‐bounding function for this larger class of graphs, and we also verify Hadwiger's conjecture for it.