Algorithms for unipolar and generalized split graphs
نویسندگان
چکیده
منابع مشابه
Algorithms for Unipolar and Generalized Split Graphs
A graph G = (V,E) is a unipolar graph if there exits a partition V = V1 ∪ V2 such that, V1 is a clique and V2 induces the disjoint union of cliques. The complement-closed class of generalized split graphs are those graphs G such that either G or the complement of G is unipolar. Generalized split graphs are a large subclass of perfect graphs. In fact, it has been shown that almost all C5-free (a...
متن کاملRecognition of unipolar and generalised split graphs
A graph is unipolar if it can be partitioned into a clique and a disjoint union of cliques, and a graph is a generalised split graph if it or its complement is unipolar. A unipolar partition of a graph can be used to find efficiently the clique number, the stability number, the chromatic number, and to solve other problems that are hard for general graphs. We present an O(n)-time algorithm for ...
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We discuss matrix partition problems for graphs that admit a partition into k independent sets and ` cliques. We show that when k + ` 6 2, any matrix M has finitely many (k, `) minimal obstructions and hence all of these problems are polynomial time solvable. We provide upper bounds for the size of any (k, `) minimal obstruction when k = ` = 1 (split graphs), when k = 2, ` = 0 (bipartite graphs...
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A graph G is called a ( p, q)-split graph if its vertex set can be partitioned into A, B so that the order of the largest independent set in A is at most p and the order of the largest complete subgraph in B is at most q. Applying a well-known theorem of Erdo s and Rado for 2-systems, it is shown that for fixed p, q, ( p, q)-split graphs can be characterized by excluding a finite set of forbidd...
متن کاملOn Chordal-k-Generalized Split Graphs
A graph G is a chordal-k-generalized split graph if G is chordal and there is a clique Q in G such that every connected component in G[V \ Q] has at most k vertices. Thus, chordal-1-generalized split graphs are exactly the split graphs. We characterize chordal-k-generalized split graphs by forbidden induced subgraphs. Moreover, we characterize a very special case of chordal-2-generalized split ...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2014
ISSN: 0166-218X
DOI: 10.1016/j.dam.2013.08.011