Independent Sets in Classes Related to Chair/Fork-free Graphs
نویسنده
چکیده
The Maximum Weight Independent Set (MWIS) problem on graphs with vertex weights asks for a set of pairwise nonadjacent vertices of maximum total weight. MWIS is known to be NP -complete in general, even under various restrictions. Let Si,j,k be the graph consisting of three induced paths of lengths i, j, k with a common initial vertex. The complexity of the MWIS problem for S1,2,2-free graphs, and for S1,1,3-free graphs are open. In this paper, we show that the MWIS problem can solved in polynomial time for (S1,2,2, S1,1,3, cochair)-free graphs, by analyzing the structure of the subclasses of this class of graphs. This extends some known results in the literature.
منابع مشابه
Maximum weight independent set for ℓclaw-free graphs in polynomial time
The MaximumWeight Independent Set (MWIS) problem is a well-known NPhard problem. A popular way to study MWIS is to detect graph classes for which MWIS can be solved in polynomial time, with particular reference to hereditary graph classes, i.e., defined by a hereditary graph property or equivalently by forbidding one or more induced subgraphs. For graphs G1, G2, G1 + G2 denotes the disjoint uni...
متن کاملINDEPENDENT SETS OF SOME GRAPHS ASSOCIATED TO COMMUTATIVE RINGS
Let $G=(V,E)$ be a simple graph. A set $Ssubseteq V$ isindependent set of $G$, if no two vertices of $S$ are adjacent.The independence number $alpha(G)$ is the size of a maximumindependent set in the graph. In this paper we study and characterize the independent sets ofthe zero-divisor graph $Gamma(R)$ and ideal-based zero-divisor graph $Gamma_I(R)$of a commutative ring $R$.
متن کاملBounds on the Number of Vertex Independent Sets in a Graph
We consider the number of vertex independent sets i(G). In general, the problem of determining the value of i(G) is NP -complete. We present several upper and lower bounds for i(G) in terms of order, size or independence number. We obtain improved bounds for i(G) on restricted graph classes such as the bipartite graphs, unicyclic graphs, regular graphs and claw-free graphs.
متن کاملStability number of bull- and chair-free graphs revisited
De Simone showed that prime bulland chair-free graphs containing a co-diamond are either bipartite or an induced cycle of odd length at least 6ve. Based on this result, we give a complete structural characterization of prime (bull,chair)-free graphs having stability number at least four as well as of (bull,chair,co-chair)-free graphs. This implies constant-bounded clique width for these graph c...
متن کاملOn variations of P4-sparse graphs
Hoàng defined the P4-sparse graphs as the graphs where every set of five vertices induces at most one P4. These graphs attracted considerable attention in connection with the P4-structure of graphs and the fact that P4-sparse graphs have bounded clique-width. Fouquet and Giakoumakis generalized this class to the nicely structured semi-P4-sparse graphs being the (P5, co-P5, co-chair)-free 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
عنوان ژورنال:
- CoRR
دوره abs/1603.02011 شماره
صفحات -
تاریخ انتشار 2016