On clique partitions of split graphs
نویسندگان
چکیده
منابع مشابه
Clique Partitions of Glued Graphs
A glued graph at K2-clone (K3-clone) results from combining two vertex-disjoint graphs by identifying an edge (a triangle) of each original graph. The clique covering numbers of these desired glued graphs have been investigated recently. Analogously, we obtain bounds of the clique partition numbers of glued graphs at K2-clones and K3-clones in terms of the clique partition numbers of their orig...
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In this paper, we prove that for any forest F ⊂ Kn, the edges of E(Kn)\E(F ) can be partitioned into O(n log n) cliques. This extends earlier results on clique partitions of the complement of a perfect matching and of a hamiltonian path in Kn. We also show that if a graph G has maximum degree 4, then the edges of E(Kn)\E(G) can be partitioned into roughly n 3 24 1 2 log n cliques provided there...
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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...
متن کاملMatrix Partitions of Split Graphs
Matrix partition problems generalize a number of natural graph partition problems, and have been studied for several standard graph classes. We prove that each matrix partition problem has only finitely many minimal obstructions for split graphs. Previously such a result was only known for the class of cographs. (In particular, there are matrix partition problems which have infinitely many mini...
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A clique in a graph G is a complete subgraph of G. A clique covering (partition) of G is a collection C of cliques such that each edge of G occurs in at least (exactly) one clique in C. The clique covering (partition) number cc(G) (cp(G)) of G is the minimum size of a clique covering (partition) of G. This paper gives alternative proofs, using a unified approach, for the results on the clique c...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1991
ISSN: 0012-365X
DOI: 10.1016/0012-365x(91)90297-f