On the structure of (claw,bull)-free graphs
Combinatorics
2019-01-03 v1
Abstract
In this research, we determine the structure of (claw, bull)-free graphs. We show that every connected (claw, bull)-free graph is either an expansion of a path, an expansion of a cycle, or the complement of a triangle-free graph; where an expansion of a graph is obtained by replacing its vertices with disjoint cliques and adding all edges between cliques corresponding to adjacent vertices of . This result also reveals facts about the structure of triangle-free graphs, which might be of independent interest.
Cite
@article{arxiv.1901.00043,
title = {On the structure of (claw,bull)-free graphs},
author = {Sebastián González Hermosillo de la Maza and Yifan Jing and Masood Masjoody},
journal= {arXiv preprint arXiv:1901.00043},
year = {2019}
}
Comments
keywords: graph classes, (claw, bull)-free, triangle-free