English

An Improved Bound for Upper Domination of Cartesian Products of Graphs

Combinatorics 2017-03-20 v1

Abstract

In this paper, we prove a problem proposed by Bre\v{s}ar: for any graphs GG and HH, Γ(GH)Γ(G)Γ(H)+min{V(G)Γ(G),V(H)Γ(H)}\Gamma(G\square H)\ge\Gamma(G)\Gamma(H)+ \min\{|V(G)|-\Gamma(G),|V(H)|-\Gamma(H)\}, where Γ(G)\Gamma(G) denotes the upper domination number of GG.

Keywords

Cite

@article{arxiv.1703.05861,
  title  = {An Improved Bound for Upper Domination of Cartesian Products of Graphs},
  author = {Yu-Yen Chien},
  journal= {arXiv preprint arXiv:1703.05861},
  year   = {2017}
}