Pavol Hell
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
Pavol Hell has a total of 79 co-authors. Here are the top co-authors by number of shared publications:
- Tomás Feder
268 Waverley St. Palo Alto USA
12 shared publications - César Hernández-Cruz
Facultad de Ciencias Universidad Nacional Autónoma de México
9 shared publications - Jing Huang
Department of Mathematics and Statistics, University of Victoria, P.O. Box 3060 STN CSC, Victoria, B.C., Canada, V8W 3R4
8 shared publications - Richard C. Brewster
Department of Mathematics and Statistics Thompson Rivers University Kamloops British Columbia Canada
8 shared publications - Jan Bok
Charles University
7 shared publications - Jaroslav Nešetřil
Computer Science Institute of Charles University
7 shared publications
Latest Publications
- Open Access
Strong chordality in tournaments and multipartite tournaments with possible loops
Strongly chordal digraphs are included in the class of chordal digraphs and generalize strongly chordal graphs and chordal bipartite graphs. They are the digraphs that admit a linear ordering of its vertex set for which their adjacency matrix does not contain the $Γ$ matrix as a submatrix. In general, it is not clear if these digraphs can be recognized in polynomial time. We focus on multipartite tournaments with possible loops. We give a polynomial-time recognition algorithm and a forbidden induced subgraph characterization of the strong chordality for each of the following cases: tournaments with possible loops, reflexive multipartite tournaments, irreflexive bipartite tournaments, irreflexive tournaments minus one arc, and balanced digraphs. In addition, we prove that in a strongly chordal digraph the minimum size of a total dominating set equals the maximum number of disjoint in-neighborhoods, and this number can be calculated in linear time given a $Γ$-free ordering of the input graph.Open AccessStrong chordality in tournaments and multipartite tournaments with possible loops
Strongly chordal digraphs are included in the class of chordal digraphs and generalize strongly chordal graphs and chordal bipartite graphs. They are the digraphs that admit a linear ordering of its vertex set for which their adjacency matrix does not contain the $Γ$ matrix as a submatrix. In general, it is not clear if these digraphs can be recognized in polynomial time. We focus on multipartite tournaments with possible loops. We give a polynomial-time recognition algorithm and a forbidden induced subgraph characterization of the strong chordality for each of the following cases: tournaments with possible loops, reflexive multipartite tournaments, irreflexive bipartite tournaments, irreflexive tournaments minus one arc, and balanced digraphs. In addition, we prove that in a strongly chordal digraph the minimum size of a total dominating set equals the maximum number of disjoint in-neighborhoods, and this number can be calculated in linear time given a $Γ$-free ordering of the input graph. - Open Access
- 5 October 2024
- Published by University of Primorska Press in The Art of Discrete and Applied Mathematics
- Vol. 7 (2) , #P2.09
Trees with minimum weighted Szeged index
The Art of Discrete and Applied Mathematics (ADAM) is a modern, dynamic, platinum open access, electronic journal that will publish high-quality articles of arbitrary length in contemporary discrete and applied mathematics in which neither the authors nor the readers incur any costs.
- 5 October 2024
- Published by University of Primorska Press in The Art of Discrete and Applied Mathematics
- Vol. 7 (2) , #P2.09
Open AccessTrees with minimum weighted Szeged index
The Art of Discrete and Applied Mathematics (ADAM) is a modern, dynamic, platinum open access, electronic journal that will publish high-quality articles of arbitrary length in contemporary discrete and applied mathematics in which neither the authors nor the readers incur any costs.
- Open Access
List homomorphisms to separable signed graphs
The complexity of the list homomorphism problem for signed graphs appears difficult to classify. Existing results focus on special classes of signed graphs, such as trees and reflexive signed graphs. Irreflexive signed graphs are in a certain sense the heart of the problem, as noted by a recent paper of Kim and Siggers. We focus on a special class of irreflexive signed graphs, namely those in which the unicoloured edges form a spanning path or cycle, which we call separable signed graphs. We classify the complexity of list homomorphisms to these separable signed graphs; we believe that these signed graphs will play an important role for the general resolution of the irreflexive case. We also relate our results to a conjecture of Kim and Siggers concerning the special case of semi-balanced irreflexive signed graphs; we have proved the conjecture in another paper, and the present results add structural information to that topic.
Open AccessList homomorphisms to separable signed graphs
The complexity of the list homomorphism problem for signed graphs appears difficult to classify. Existing results focus on special classes of signed graphs, such as trees and reflexive signed graphs. Irreflexive signed graphs are in a certain sense the heart of the problem, as noted by a recent paper of Kim and Siggers. We focus on a special class of irreflexive signed graphs, namely those in which the unicoloured edges form a spanning path or cycle, which we call separable signed graphs. We classify the complexity of list homomorphisms to these separable signed graphs; we believe that these signed graphs will play an important role for the general resolution of the irreflexive case. We also relate our results to a conjecture of Kim and Siggers concerning the special case of semi-balanced irreflexive signed graphs; we have proved the conjecture in another paper, and the present results add structural information to that topic.
- 18 April 2024
- Published by Elsevier in Theoretical Computer Science
- Vol. 1001
List homomorphisms to separable signed graphs
- 18 April 2024
- Published by Elsevier in Theoretical Computer Science
- Vol. 1001
List homomorphisms to separable signed graphs
- 12 April 2024
- Published by Springer Nature in Algorithmica
- Vol. 86 (7) , 2289-2316
Min Orderings and List Homomorphism Dichotomies for Graphs and Signed Graphs
- 12 April 2024
- Published by Springer Nature in Algorithmica
- Vol. 86 (7) , 2289-2316
Min Orderings and List Homomorphism Dichotomies for Graphs and Signed Graphs
- 6 March 2024
- Published by Springer Nature
- p. 31-45
Bi-arc Digraphs: Recognition Algorithm and Applications
- 6 March 2024
- Published by Springer Nature
- p. 31-45
Bi-arc Digraphs: Recognition Algorithm and Applications
- Open Access
List homomorphism problems for signed trees
We consider homomorphisms of signed graphs from a computational perspective. In particular, we study the list homomorphism problem seeking a homomorphism of an input signed graph $(G,\sigma)$, equipped with lists $L(v) \subseteq V(H), v \in V(G)$, of allowed images, to a fixed target signed graph $(H,\pi)$. The complexity of the similar homomorphism problem without lists (corresponding to all lists being $L(v)=V(H)$) has been previously classified by Brewster and Siggers, but the list version remains open and appears difficult. We illustrate this difficulty by classifying the complexity of the problem when $H$ is a tree (with possible loops). The tools we develop will be useful for classifications of other classes of signed graphs, and in a future companion paper we will illustrate this by using them to classify the complexity for certain irreflexive signed graphs. The structure of the signed trees in the polynomial cases is interesting, suggesting that the class of general signed graphs for which the problems are polynomial may have nice structure, analogous to the so-called bi-arc graphs (which characterized the polynomial cases of list homomorphisms to unsigned graphs).Open AccessList homomorphism problems for signed trees
We consider homomorphisms of signed graphs from a computational perspective. In particular, we study the list homomorphism problem seeking a homomorphism of an input signed graph $(G,\sigma)$, equipped with lists $L(v) \subseteq V(H), v \in V(G)$, of allowed images, to a fixed target signed graph $(H,\pi)$. The complexity of the similar homomorphism problem without lists (corresponding to all lists being $L(v)=V(H)$) has been previously classified by Brewster and Siggers, but the list version remains open and appears difficult. We illustrate this difficulty by classifying the complexity of the problem when $H$ is a tree (with possible loops). The tools we develop will be useful for classifications of other classes of signed graphs, and in a future companion paper we will illustrate this by using them to classify the complexity for certain irreflexive signed graphs. The structure of the signed trees in the polynomial cases is interesting, suggesting that the class of general signed graphs for which the problems are polynomial may have nice structure, analogous to the so-called bi-arc graphs (which characterized the polynomial cases of list homomorphisms to unsigned graphs). - 30 November 2022
- Published by Elsevier in Discrete Mathematics
- Vol. 346 (3)
List homomorphism problems for signed trees
- 30 November 2022
- Published by Elsevier in Discrete Mathematics
- Vol. 346 (3)
List homomorphism problems for signed trees
- Open Access
Strong cocomparability graphs and Slash-free orderings of matrices
We introduce the class of strong cocomparability graphs, as the class of reflexive graphs whose adjacency matrix can be rearranged by a simultaneous row and column permutation to avoid the submatrix with rows 01, 10, which we call Slash. We provide an ordering characterization, a forbidden structure characterization, and a polynomial-time recognition algorithm, for the class. These results complete the picture in which in addition to, or instead of, the Slash matrix one forbids the Gamma matrix (which has rows 11, 10). It is well known that in these two cases one obtains the class of interval graphs, and the class of strongly chordal graphs, respectively. By complementation, we obtain the class of strong comparability graphs, whose adjacency matrix can be rearranged by a simultaneous row and column permutation to avoid the two-by-two identity submatrix. Thus our results give characterizations and algorithms for this class of irreflexive graphs as well. In other words, our results may be interpreted as solving the following problem: given a symmetric 0,1-matrix with 0-diagonal, can the rows and columns of be simultaneously permuted to avoid the two-by-two identity submatrix?
Open AccessStrong cocomparability graphs and Slash-free orderings of matrices
We introduce the class of strong cocomparability graphs, as the class of reflexive graphs whose adjacency matrix can be rearranged by a simultaneous row and column permutation to avoid the submatrix with rows 01, 10, which we call Slash. We provide an ordering characterization, a forbidden structure characterization, and a polynomial-time recognition algorithm, for the class. These results complete the picture in which in addition to, or instead of, the Slash matrix one forbids the Gamma matrix (which has rows 11, 10). It is well known that in these two cases one obtains the class of interval graphs, and the class of strongly chordal graphs, respectively. By complementation, we obtain the class of strong comparability graphs, whose adjacency matrix can be rearranged by a simultaneous row and column permutation to avoid the two-by-two identity submatrix. Thus our results give characterizations and algorithms for this class of irreflexive graphs as well. In other words, our results may be interpreted as solving the following problem: given a symmetric 0,1-matrix with 0-diagonal, can the rows and columns of be simultaneously permuted to avoid the two-by-two identity submatrix?
- 29 October 2022
- Published by Springer Nature
- p. 510-526
Min Orderings and List Homomorphism Dichotomies for Signed and Unsigned Graphs
- 29 October 2022
- Published by Springer Nature
- p. 510-526
Min Orderings and List Homomorphism Dichotomies for Signed and Unsigned Graphs