On equistable, split, CIS, and related classes of graphs

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Abstract

We consider several graphs classes defined in terms of conditions on cliques and stable sets, including CIS, split, equistable, and other related classes. We pursue a systematic study of the relations between them. As part of this study, we introduce two generalizations of CIS graphs, obtain a new characterization of split graphs, and a characterization of CIS line graphs.

Keywords

Clique
Stable set
CIS graph
Equistable graph
Split graph
Triangle condition
General partition graph
Edge simplicial graph
Upper bound graph
Normal graph

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The first author thanks for partial support the National Science Foundation (Grant No. IIS-1161476). This work is supported in part also by the Slovenian Research Agency (I0-0035, research program P1-0285 and research projects BI-US/14–15–050, N1-0032, J1-5433, J1-6720, and J1-6743).