Paloma T. Lima
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
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Research Interests
Paloma T. Lima has a total of 23 co-authors. Here are the top co-authors by number of shared publications:
- Petr A. Golovach
Department of Informatics, University of Bergen
6 shared publications - Lars Jaffke
NHH Norwegian School of Economics, Bergen, Norway
5 shared publications - Pinar Heggernes
Univ Bergen, Dept Informat, N-5020 Bergen, Norway
5 shared publications - Daniël Paulusma
Durham University, Durham, UK
4 shared publications - Bernard Ries
Department of Informatics, University of Fribourg, Fribourg, Switzerland
3 shared publications - Charis Papadopoulos
Department of Mathematics University of Ioannina Greece
3 shared publications
Latest Publications
- Open Access
b-Coloring Parameterized by Clique-Width
We provide a polynomial-time algorithm for b-Coloring on graphs of constant clique-width. This unifies and extends nearly all previously known polynomial time results on graph classes, and answers open questions posed by Campos and Silva [Algorithmica, 2018] and Bonomo et al. [Graphs Combin., 2009]. This constitutes the first result concerning structural parameterizations of this problem. We show that the problem is FPT when parameterized by the vertex cover number on general graphs, and on chordal graphs when parameterized by the number of colors. Additionally, we observe that our algorithm for graphs of bounded clique-width can be adapted to solve the Fall Coloring problem within the same runtime bound. The running times of the clique-width based algorithms for b-Coloring and Fall Coloring are tight under the Exponential Time Hypothesis.
Open Accessb-Coloring Parameterized by Clique-Width
We provide a polynomial-time algorithm for b-Coloring on graphs of constant clique-width. This unifies and extends nearly all previously known polynomial time results on graph classes, and answers open questions posed by Campos and Silva [Algorithmica, 2018] and Bonomo et al. [Graphs Combin., 2009]. This constitutes the first result concerning structural parameterizations of this problem. We show that the problem is FPT when parameterized by the vertex cover number on general graphs, and on chordal graphs when parameterized by the number of colors. Additionally, we observe that our algorithm for graphs of bounded clique-width can be adapted to solve the Fall Coloring problem within the same runtime bound. The running times of the clique-width based algorithms for b-Coloring and Fall Coloring are tight under the Exponential Time Hypothesis.
- Open Access
- 29 November 2021
- Published by Springer Nature in Algorithmica
- Vol. 84 (2) , 273-303
Structural Parameterizations of Clique Coloring
A clique coloring of a graph is an assignment of colors to its vertices such that no maximal clique is monochromatic. We initiate the study of structural parameterizations of the Clique Coloring problem which asks whether a given graph has a clique coloring with q colors. For fixed $$q \ge 2$$ , we give an $$\mathscr {O}^{\star }(q^{{\mathsf {tw}}})$$ -time algorithm when the input graph is given together with one of its tree decompositions of width $${\mathsf {tw}} $$ . We complement this result with a matching lower bound under the Strong Exponential Time Hypothesis. We furthermore show that (when the number of colors is unbounded) Clique Coloring is $$\mathsf {XP}$$ parameterized by clique-width.- 29 November 2021
- Published by Springer Nature in Algorithmica
- Vol. 84 (2) , 273-303
Open AccessStructural Parameterizations of Clique Coloring
A clique coloring of a graph is an assignment of colors to its vertices such that no maximal clique is monochromatic. We initiate the study of structural parameterizations of the Clique Coloring problem which asks whether a given graph has a clique coloring with q colors. For fixed $$q \ge 2$$ , we give an $$\mathscr {O}^{\star }(q^{{\mathsf {tw}}})$$ -time algorithm when the input graph is given together with one of its tree decompositions of width $${\mathsf {tw}} $$ . We complement this result with a matching lower bound under the Strong Exponential Time Hypothesis. We furthermore show that (when the number of colors is unbounded) Clique Coloring is $$\mathsf {XP}$$ parameterized by clique-width. - Open Access
Reducing graph transversals via edge contractions
For a graph invariant $\pi$, the Contraction($\pi$) problem consists in, given a graph $G$ and two positive integers $k,d$, deciding whether one can contract at most $k$ edges of $G$ to obtain a graph in which $\pi$ has dropped by at least $d$. Galby et al. [ISAAC 2019, MFCS 2019] recently studied the case where $\pi$ is the size of a minimum dominating set. We focus on graph invariants defined as the minimum size of a vertex set that hits all the occurrences of graphs in a collection ${\cal H}$ according to a fixed containment relation. We prove co-NP-hardness results under some assumptions on the graphs in ${\cal H}$, which in particular imply that Contraction($\pi$) is co-NP-hard even for fixed $k=d=1$ when $\pi$ is the size of a minimum feedback vertex set or an odd cycle transversal. In sharp contrast, we show that when $\pi$ is the size of a minimum vertex cover, the problem is in XP parameterized by $d$.Open AccessReducing graph transversals via edge contractions
For a graph invariant $\pi$, the Contraction($\pi$) problem consists in, given a graph $G$ and two positive integers $k,d$, deciding whether one can contract at most $k$ edges of $G$ to obtain a graph in which $\pi$ has dropped by at least $d$. Galby et al. [ISAAC 2019, MFCS 2019] recently studied the case where $\pi$ is the size of a minimum dominating set. We focus on graph invariants defined as the minimum size of a vertex set that hits all the occurrences of graphs in a collection ${\cal H}$ according to a fixed containment relation. We prove co-NP-hardness results under some assumptions on the graphs in ${\cal H}$, which in particular imply that Contraction($\pi$) is co-NP-hard even for fixed $k=d=1$ when $\pi$ is the size of a minimum feedback vertex set or an odd cycle transversal. In sharp contrast, we show that when $\pi$ is the size of a minimum vertex cover, the problem is in XP parameterized by $d$. - 3 December 2020
- Published by Springer Nature
- p. 600-612
On the Maximum Number of Edges in Chordal Graphs of Bounded Degree and Matching Number
- 3 December 2020
- Published by Springer Nature
- p. 600-612
On the Maximum Number of Edges in Chordal Graphs of Bounded Degree and Matching Number
- 1 November 2020
- Published by Elsevier in Journal of Computer and System Sciences
- Vol. 113, 101-124
Finding connected secluded subgraphs
- 1 November 2020
- Published by Elsevier in Journal of Computer and System Sciences
- Vol. 113, 101-124
Finding connected secluded subgraphs
- Open Access
Graph Square Roots of Small Distance from Degree One Graphs
Given a graph class $\mathcal{H}$, the task of the $\mathcal{H}$-Square Root problem is to decide, whether an input graph $G$ has a square root $H$ from $\mathcal{H}$. We are interested in the parameterized complexity of the problem for classes $\mathcal{H}$ that are composed by the graphs at vertex deletion distance at most $k$ from graphs of maximum degree at most one, that is, we are looking for a square root $H$ such that there is a modulator $S$ of size $k$ such that $H-S$ is the disjoint union of isolated vertices and disjoint edges. We show that different variants of the problems with constraints on the number of isolated vertices and edges in $H-S$ are FPT when parameterized by $k$ by demonstrating algorithms with running time $2^{2^{O(k)}}\cdot n^{O(1)}$. We further show that the running time of our algorithms is asymptotically optimal and it is unlikely that the double-exponential dependence on $k$ could be avoided. In particular, we prove that the VC-$k$ Root problem, that asks whether an input graph has a square root with vertex cover of size at most $k$, cannot be solved in time $2^{2^{o(k)}}\cdot n^{O(1)}$ unless Exponential Time Hypothesis fails. Moreover, we point out that VC-$k$ Root parameterized by $k$ does not admit a subexponential kernel unless $P=NP$.Open AccessGraph Square Roots of Small Distance from Degree One Graphs
Given a graph class $\mathcal{H}$, the task of the $\mathcal{H}$-Square Root problem is to decide, whether an input graph $G$ has a square root $H$ from $\mathcal{H}$. We are interested in the parameterized complexity of the problem for classes $\mathcal{H}$ that are composed by the graphs at vertex deletion distance at most $k$ from graphs of maximum degree at most one, that is, we are looking for a square root $H$ such that there is a modulator $S$ of size $k$ such that $H-S$ is the disjoint union of isolated vertices and disjoint edges. We show that different variants of the problems with constraints on the number of isolated vertices and edges in $H-S$ are FPT when parameterized by $k$ by demonstrating algorithms with running time $2^{2^{O(k)}}\cdot n^{O(1)}$. We further show that the running time of our algorithms is asymptotically optimal and it is unlikely that the double-exponential dependence on $k$ could be avoided. In particular, we prove that the VC-$k$ Root problem, that asks whether an input graph has a square root with vertex cover of size at most $k$, cannot be solved in time $2^{2^{o(k)}}\cdot n^{O(1)}$ unless Exponential Time Hypothesis fails. Moreover, we point out that VC-$k$ Root parameterized by $k$ does not admit a subexponential kernel unless $P=NP$. - Open Access
Algorithms for the rainbow vertex coloring problem on graph classes
Given a vertex-colored graph, we say a path is a rainbow vertex path if all its internal vertices have distinct colors. The graph is rainbow vertex-connected if there is a rainbow vertex path between every pair of its vertices. In the Rainbow Vertex Coloring (RVC) problem we want to decide whether the vertices of a given graph can be colored with at most $k$ colors so that the graph becomes rainbow vertex-connected. This problem is known to be NP-complete even in very restricted scenarios, and very few efficient algorithms are known for it. In this work, we give polynomial-time algorithms for RVC on permutation graphs, powers of trees and split strongly chordal graphs. The algorithm for the latter class also works for the strong variant of the problem, where the rainbow vertex paths between each vertex pair must be shortest paths. We complement the polynomial-time solvability results for split strongly chordal graphs by showing that, for any fixed $p\geq 3$ both variants of the problem become NP-complete when restricted to split $(S_3,\ldots,S_p)$-free graphs, where $S_q$ denotes the $q$-sun graph.Open AccessAlgorithms for the rainbow vertex coloring problem on graph classes
Given a vertex-colored graph, we say a path is a rainbow vertex path if all its internal vertices have distinct colors. The graph is rainbow vertex-connected if there is a rainbow vertex path between every pair of its vertices. In the Rainbow Vertex Coloring (RVC) problem we want to decide whether the vertices of a given graph can be colored with at most $k$ colors so that the graph becomes rainbow vertex-connected. This problem is known to be NP-complete even in very restricted scenarios, and very few efficient algorithms are known for it. In this work, we give polynomial-time algorithms for RVC on permutation graphs, powers of trees and split strongly chordal graphs. The algorithm for the latter class also works for the strong variant of the problem, where the rainbow vertex paths between each vertex pair must be shortest paths. We complement the polynomial-time solvability results for split strongly chordal graphs by showing that, for any fixed $p\geq 3$ both variants of the problem become NP-complete when restricted to split $(S_3,\ldots,S_p)$-free graphs, where $S_q$ denotes the $q$-sun graph. - Open Access
Structural Parameterizations of Clique Coloring
A clique coloring of a graph is an assignment of colors to its vertices such that no maximal clique is monochromatic. We initiate the study of structural parameterizations of the Clique Coloring problem which asks whether a given graph has a clique coloring with $q$ colors. For fixed $q \ge 2$, we give an $\mathcal{O}^{\star}(q^{tw})$-time algorithm when the input graph is given together with one of its tree decompositions of width $tw$. We complement this result with a matching lower bound under the Strong Exponential Time Hypothesis. We furthermore show that (when the number of colors is unbounded) Clique Coloring is XP parameterized by clique-width.Open AccessStructural Parameterizations of Clique Coloring
A clique coloring of a graph is an assignment of colors to its vertices such that no maximal clique is monochromatic. We initiate the study of structural parameterizations of the Clique Coloring problem which asks whether a given graph has a clique coloring with $q$ colors. For fixed $q \ge 2$, we give an $\mathcal{O}^{\star}(q^{tw})$-time algorithm when the input graph is given together with one of its tree decompositions of width $tw$. We complement this result with a matching lower bound under the Strong Exponential Time Hypothesis. We furthermore show that (when the number of colors is unbounded) Clique Coloring is XP parameterized by clique-width. - Open Access
Well-partitioned chordal graphs: obstruction set and disjoint paths
We introduce a new subclass of chordal graphs that generalizes split graphs, which we call well-partitioned chordal graphs. Split graphs are graphs that admit a partition of the vertex set into cliques that can be arranged in a star structure, the leaves of which are of size one. Well-partitioned chordal graphs are a generalization of this concept in the following two ways. First, the cliques in the partition can be arranged in a tree structure, and second, each clique is of arbitrary size. We provide a characterization of well-partitioned chordal graphs by forbidden induced subgraphs, and give a polynomial-time algorithm that given any graph, either finds an obstruction, or outputs a partition of its vertex set that asserts that the graph is well-partitioned chordal. We demonstrate the algorithmic use of this graph class by showing that two variants of the problem of finding pairwise disjoint paths between k given pairs of vertices is in FPT parameterized by k on well-partitioned chordal graphs, while on chordal graphs, these problems are only known to be in XP. From the other end, we observe that there are problems that are polynomial-time solvable on split graphs, but become NP-complete on well-partitioned chordal graphs.
Open AccessWell-partitioned chordal graphs: obstruction set and disjoint paths
We introduce a new subclass of chordal graphs that generalizes split graphs, which we call well-partitioned chordal graphs. Split graphs are graphs that admit a partition of the vertex set into cliques that can be arranged in a star structure, the leaves of which are of size one. Well-partitioned chordal graphs are a generalization of this concept in the following two ways. First, the cliques in the partition can be arranged in a tree structure, and second, each clique is of arbitrary size. We provide a characterization of well-partitioned chordal graphs by forbidden induced subgraphs, and give a polynomial-time algorithm that given any graph, either finds an obstruction, or outputs a partition of its vertex set that asserts that the graph is well-partitioned chordal. We demonstrate the algorithmic use of this graph class by showing that two variants of the problem of finding pairwise disjoint paths between k given pairs of vertices is in FPT parameterized by k on well-partitioned chordal graphs, while on chordal graphs, these problems are only known to be in XP. From the other end, we observe that there are problems that are polynomial-time solvable on split graphs, but become NP-complete on well-partitioned chordal graphs.
- Open Access
- 5 February 2020
- Published by Springer Nature in Algorithmica
- Vol. 82 (7) , 2006-2038
Parameterized Aspects of Strong Subgraph Closure
- 5 February 2020
- Published by Springer Nature in Algorithmica
- Vol. 82 (7) , 2006-2038
Open AccessParameterized Aspects of Strong Subgraph Closure