On a clique covering problem of orlin
โ Scribed by David A. Gregory; Norman J. Pullman
- Publisher
- Elsevier Science
- Year
- 1982
- Tongue
- English
- Weight
- 261 KB
- Volume
- 41
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
โฆ Synopsis
Let Tz, be the complement of a perfect matching in the complete ,qraph on 2n vertkes, am; cc(T?,I be the minimum #lumber of complete subgraphs necessary to cover all rhe edge? cf T2,,. Orlin posed the problem of determining the asymptotic behzviour of cc(T,,!. We show that cc( T,,
๐ SIMILAR VOLUMES
For a graph G = (V,E), a vertex set XC\_ V is called a clique if Ixl>~2 and the graph G [X] induced by X is a complete subgraph maximal under inclusion. We say that a vertex set T is a clique-transversal set if T N X ~ 0 for all cliques X of G, and define the clique-transversal number re(G) as the m
The following conjecture of T. Gallai is proved: If G is a chordal graph on n vertices, such that all its maximal complete subgraphs have order at least 3, then there is a vertex set of cardinality ~n/3 which meets all maximal complete subgraphs of G. Further related results are given.
Let G be a line graph. Orlin determined the clique covering and clique partition numbers cc(G) and cp(G). We obtain a constructive proof of Orlin's result and in doing so we are able to completely enumerate the number of distinct minimal clique covers and partitions of G, in terms of easily calculab