In: Discrete Applied Mathematics, 2021, vol. 290, p. 17-35
In this paper we continue the systematic study of Contact graphs of Paths on a Grid (CPG graphs) initiated in Deniz et al. (2018). A CPG graph is a graph for which there exists a collection of pairwise interiorly disjoint paths on a grid in one-to-one correspondence with its vertex set such that two vertices are adjacent if and only if the corresponding paths touch at a grid-point. If every...
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In: Theoretical Computer Science, 2021, vol. 877, p. 18-35
In this paper, we study the problem of deciding whether the total domination number of a given graph Gcan be reduced using exactly one edge contraction (called1-Edge Contraction(γt)). We focus on several graph classes and determine the computational complexity of this problem. By putting together these results, we manage to obtain a complete complexity dichotomy for H-free graphs.
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In: Discrete Mathematics, 2021, vol. 344, no. 1, p. 112169
In this work, we study the following problem: given a connected graph G, can we reduce the domination number of G by at least one using k edge contractions, for some fixed integer k > 0? We show that for k = 1 (resp. k = 2), the problem is NP-hard (resp. coNP-hard). We further prove that for k = 1, the problem is W[1]-hard parameterized by domination number plus the mim-width of the input...
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In: Theoretical Computer Science, 2020, vol. 814, p. 28-48
A semitotal dominating set of a graph G with no isolated vertex is a dominating set D of G such that every vertex in D is within distance two of another vertex in D. The minimum size γt2(G) of a semitotal dominating set of G is squeezed between the domination number γ(G) and the total domination number γt(G). Semitotal Dominating Set is the problem of finding, given a graph G, a semitotal...
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In: 30th International Symposium on Algorithms and Computation (ISAAC) - Leibniz International Proceedings in Informatics, 2019, vol. 149, no. 21, p. 1-14
In this paper, we consider the following problem: given a connected graph G, can we reduce the domination number of G by one by using only one edge contraction? We show that the problem is NP-hard when restricted to {P6, P4 + P2}-free graphs and that it is coNP-hard when restricted to subcubic claw-free graphs and 2P3-free graphs. As a consequence, we are able to establish a complexity dichotomy...
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In: 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019) - LIPICS Vol. 138, 2019, p. 41:1-41:13
In this paper, we study the following problem: given a connected graph G, can we reduce the domination number of G by at least one using k edge contractions, for some fixed integer k >= 0? We show that for k <= 2, the problem is coNP-hard. We further prove that for k=1, the problem is W[1]-hard parameterized by the size of a minimum dominating set plus the mim-width of the input graph, and that...
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In: Discrete Applied Mathematics, 2019, vol. 262, p. 195-202
In this paper we present a characterization, by an infinite family of minimal forbidden induced subgraphs, of proper circular arc graphs which are intersection graphs of paths on a grid, where each path has at most one bend (turn).
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In: Lecture Notes in Computer Science, 2018, vol. 11282, p. 317-330
In this paper we consider Contact graphs of Paths on a Grid (CPG graphs), i.e. graphs for which there exists a family of interiorly disjoint paths on a grid in one-to-one correspondence with their vertex set such that two vertices are adjacent if and only if the corresponding paths touch at a grid-point. Our class generalizes the well studied class of VCPG graphs (see [1]). We examine CPG...
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In: Information procesing letters, 2019, vol. 146, p. 39-43
A graph is H-free if it does not contain an induced subgraph isomorphic to H. For every integer k and every graph H, we determine the computational complexity of k-Edge Colouring for H-free graphs.
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