Equistable simplicial, very well-covered, and line graphs

Vadim E. Levit; Martin Milanič

doi:10.1016/j.dam.2013.01.022

Equistable simplicial, very well-covered, and line graphs

Vadim E. Levit, Martin Milanič

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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.

Original language	English
Pages (from-to)	205-212
Number of pages	8
Journal	Discrete Applied Mathematics
Volume	165
DOIs	https://doi.org/10.1016/j.dam.2013.01.022
State	Published - 11 Mar 2014
Externally published	Yes

Keywords

Equistable graph
General partition graph
Line graph
Polynomial time algorithm
Simplicial graph
Strongly equistable graph
Triangle condition
Triangle graph
Very well-covered graph

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10.1016/j.dam.2013.01.022

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title = "Equistable simplicial, very well-covered, and line graphs",

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.",

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T1 - Equistable simplicial, very well-covered, and line graphs

AU - Levit, Vadim E.

AU - Milanič, Martin

PY - 2014/3/11

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N2 - 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.

AB - 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.

KW - Equistable graph

KW - General partition graph

KW - Line graph

KW - Polynomial time algorithm

KW - Simplicial graph

KW - Strongly equistable graph

KW - Triangle condition

KW - Triangle graph

KW - Very well-covered graph

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SN - 0166-218X

VL - 165

SP - 205

EP - 212

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

Equistable simplicial, very well-covered, and line graphs

Abstract

Keywords

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