Equistable simplicial, very well-covered, and line graphs

Authors:
Vadim E. Levit;Martin Milanič
Affiliations:
Department of Computer Science and Mathematics, Ariel University of Samaria, Ariel 40700, Israel;University of Primorska, UP IAM, Muzejski trg 2, SI6000 Koper, Slovenia and University of Primorska, UP FAMNIT, Glagoljaška 8, SI6000 Koper, Slovenia
Venue:
Discrete Applied Mathematics
Year:
2014

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Abstract

We verify the conjectures of Mahadev-Peled-Sun and of Orlin, both related to equistable graphs, for the classes of simplicial, very well-covered and line graphs. Our results are based on the combinatorial features of triangle graphs and general partition graphs. In particular, we obtain several equivalent characterizations of equistable simplicial graphs, equistable very well-covered graphs, and equistable line graphs, some of which imply polynomial time recognition algorithms for graphs in these classes.