On equistable, split, CIS, and related classes of graphs
نویسندگان
چکیده
منابع مشابه
On equistable, split, CIS, and related classes of graphs
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.
متن کاملStructural Results for Equistable Graphs and Related Graph Classes
The class of equistable graphs is defined by the existence of a weight structure on the vertices where maximal stable sets are characterized by their weights. This class, not contained in any nontrivial hereditary class, has been studied both from a structural and an algorithmic point of view, however no combinatorial characterization is known for these graphs. We present some structural result...
متن کاملComplexity results for equistable graphs and related classes
The class of equistable graphs is defined by the existence of a cost structure on the vertices such that the maximal stable sets are characterized by their costs. This graph class, not contained in any nontrivial hereditary class, has so far been studied mostly from a structural point of view; characterizations and polynomial time recognition algorithms have been obtained for special cases. We ...
متن کاملOn split and almost CIS-graphs
A CIS-graph is defined as a graph whose every maximal clique and stable set intersect. These graphs have many interesting properties, yet, it seems difficult to obtain an efficient characterization and/or polynomial-time recognition algorithm for CIS-graphs. An almost CIS-graph is defined as a graph that has a unique pair (C, S) of disjoint maximal clique C and stable sets S. We conjecture that...
متن کاملEquistable series-parallel graphs
A graph is called equistable when there is a non-negative weight function on its vertices such that a set S of vertices has total weight 1 if and only if S is maximal stable. We characterize those series-parallel graphs that are equistable, generalizing results of Mahadev, Peled and Sun about equistable outer-planar graphs.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2017
ISSN: 0166-218X
DOI: 10.1016/j.dam.2015.07.023