On Equistable, Split, CIS, and Related Classes of Graphs
Endre Boros, Vladimir Gurvich, Martin Milani\v{c}
TL;DR
This paper systematically explores various graph classes defined by clique and stable set conditions, introducing new generalizations and characterizations to deepen understanding of their relationships.
Contribution
It introduces two generalizations of CIS graphs, provides a new characterization of split graphs, and characterizes CIS line graphs, advancing theoretical understanding of these classes.
Findings
Introduced two generalizations of CIS graphs
Provided a new characterization of split graphs
Characterized CIS line graphs
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.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph theory and applications · Graph Labeling and Dimension Problems