TY - JOUR
T1 - Equistable simplicial, very well-covered, and line graphs
AU - Levit, Vadim E.
AU - Milanič, Martin
PY - 2014/3/11
Y1 - 2014/3/11
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
UR - http://www.scopus.com/inward/record.url?scp=84893758985&partnerID=8YFLogxK
U2 - 10.1016/j.dam.2013.01.022
DO - 10.1016/j.dam.2013.01.022
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AN - SCOPUS:84893758985
SN - 0166-218X
VL - 165
SP - 205
EP - 212
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
ER -