On chromatic vertex stability of 3-chromatic graphs with maximum degree 4

Martin Knor; Mirko Petruševski; Riste Škrekovski

On chromatic vertex stability of 3-chromatic graphs with maximum degree 4

Combinatorics 2022-05-05 v1

Authors: Martin Knor , Mirko Petruševski , Riste Škrekovski

Abstract

The (independent) chromatic vertex stability ( $\ivs(G)$ ) $\vs(G)$ is the minimum size of (independent) set $S\subseteq V(G)$ such that $\chi(G-S)=\chi(G)-1$ . In this paper we construct infinitely many graphs $G$ with $\Delta(G)=4$ , $\chi(G)=3$ , $\ivs(G)=3$ and $\vs(G)=2$ , which gives a partial negative answer to a problem posed in \cite{ABKM}.

Keywords

chromatic vertex stability independent vertex stability 3-chromatic graphs maximum degree 4 graph coloring

Cite

@article{arxiv.2205.01976,
  title  = {On chromatic vertex stability of 3-chromatic graphs with maximum degree 4},
  author = {Martin Knor and Mirko Petruševski and Riste Škrekovski},
  journal= {arXiv preprint arXiv:2205.01976},
  year   = {2022}
}

Comments

7 pages, 4 figures

Related papers

View all related →