منابع مشابه
Clique 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...
متن کاملGeneralized covering designs and clique coverings
Inspired by the “generalized t-designs” defined by Cameron [P. J. Cameron, A generalisation of t-designs, Discrete Math. 309 (2009), 4835–4842], we define a new class of combinatorial designs which simultaneously provide a generalization of both covering designs and covering arrays. We then obtain a number of bounds on the minimum sizes of these designs, and describe some methods of constructin...
متن کاملClique Partitions of Dense Graphs
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...
متن کاملClique partitions of distance multigraphs
We consider the minimum number of cliques needed to partition the edge set of D(G), the distance multigraph of a simple graph G. Equivalently, we seek to minimize the number of elements needed to label the vertices of a simple graph G by sets so that the distance between two vertices equals the cardinality of the intersection of their labels. We use a fractional analogue of this parameter to fi...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1988
ISSN: 0012-365X
DOI: 10.1016/0012-365x(88)90197-5