Blocking dominating sets for $H$-free graphs via edge contractions

Esther Galby; Paloma T. Lima; Bernard Ries

Blocking dominating sets for $H$-free graphs via edge contractions

Discrete Mathematics 2019-08-06 v2 Computational Complexity Combinatorics

Authors: Esther Galby , Paloma T. Lima , Bernard Ries

Abstract

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 $\mathsf{NP}$ -hard when restricted to $\{P_6,P_4+P_2\}$ -free graphs and that it is $\mathsf{coNP}$ -hard when restricted to subcubic claw-free graphs and $2P_3$ -free graphs. As a consequence, we are able to establish a complexity dichotomy for the problem on $H$ -free graphs when $H$ is connected.

Keywords

graph homomorphism graph theory planar graph drawing

Cite

@article{arxiv.1906.12297,
  title  = {Blocking dominating sets for $H$-free graphs via edge contractions},
  author = {Esther Galby and Paloma T. Lima and Bernard Ries},
  journal= {arXiv preprint arXiv:1906.12297},
  year   = {2019}
}

Comments

arXiv admin note: text overlap with arXiv:1903.01800

Blocking dominating sets for $H$-free graphs via edge contractions

Abstract

Keywords

Cite

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