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On a clique covering problem of orlin

โœ 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

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โœฆ 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,,


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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