On the number of distinct minimal clique partitions and clique covers of a line graph
نویسندگان
چکیده
منابع مشابه
Clique partitions of the cocktail party graph
For our purposes, graphs have no loops or multiple edges. Aside from this, our terminology follows that of Bondy and Murty [1]. A clique is a complete subgraph. A clique partition of a graph G is a family ~ of cliques of G such that each edge of G is in precisely one member of q¢. The clique partition number, cp(G), is the minimum of the cardinalities of the clique partitions of G. Let To denot...
متن کاملClique partitions and clique coverings
Several new tools are presented for determining the number of cliques needed to (edge-)partition a graph . For a graph on n vertices, the clique partition number can grow cn z times as fast as the clique covering number, where c is at least 1/64. If in a clique on n vertices, the edges between en° vertices are deleted, Z--a < 1, then the number of cliques needed to partition what is left is asy...
متن کاملClique coverings and partitions of line graphs
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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We rst consider the problem of partitioning the edges of a graph G into bipartite cliques such that the total order of the cliques is minimized, where the order of a clique is the number of vertices in it. It is shown that the problem is NP-complete. We then prove the existence of a partition of small total order in a suuciently dense graph and devise an eecient algorithm to compute such a part...
متن کاملOn the connection between chromatic number, maximal clique and minimal degree of a graph
Let G n be a graph of n vertices, having chromatic number r which contains no complete graph of r vertices . Then G n contains a vertex of degree not exceeding n(3r-7)í(3r-4). The result is essentially best possible .
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1990
ISSN: 0012-365X
DOI: 10.1016/0012-365x(90)90220-c