Equistable graphs, general partition graphs, triangle graphs, and graph products
نویسندگان
چکیده
منابع مشابه
Structural Results for General Partition, Equistable and Triangle graphs
Miklavič and Milanič (2011) introduced the connections among the classes of equistable, general partition and triangle graphs. We present results concerning the three classes aforementioned. In particular, we show that the general partition and triangle classes are both closed under the operations of substitution, induction and contraction of modules. Moreover, we show that the triangle conditi...
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 کاملEquistable Chordal 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 show that a chordal graphs is equistable if and only if every two adjacent non-simplicial vertices have a common simplicial neighbor.
متن کاملEquistable distance-hereditary graphs
A graph is called equistable when there is a nonnegative 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 show that a necessary condition for a graph to be equistable is sufficient when the graph in question is distance-hereditary. This is used to design a polynomial-time recognition algorithm for equistable distanceheredita...
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 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: 2011
ISSN: 0166-218X
DOI: 10.1016/j.dam.2011.03.011