Connected Dominating Sets in Graphs With Stability Number Three
Combinatorics
2017-03-21 v1
Abstract
In the special case of graphs G of independence number a(G)=3 without induced chordless cycles C7 it is shown that exists connected dominating set D of vertices with number of vertices n(D)<=4. Using the concept of connected dominating sets, we defined a new invariant h(G) that does not exceed the number of Hadwiger. For the considered graphs it is shown that h(G)>=n(G)/4.
Cite
@article{arxiv.1703.06556,
title = {Connected Dominating Sets in Graphs With Stability Number Three},
author = {Vladimir Bercov},
journal= {arXiv preprint arXiv:1703.06556},
year = {2017}
}