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|Abstract:||Let C be a clique of a graph G. The capacity of C is defined to be (|V (G)\textbackslashC|+|D|)/2, where D is the set of vertices in V (G)\textbackslashC that have both a neighbour and a non-neighbour in C. We give a polynomial-time algorithm to find the minimum clique capacity in a graph G. This problem arose in the study  of packing vertex-disjoint induced three-vertex paths in a graph with no stable set of size three, which in turn was motivated by Hadwiger’s conjecture.|
|Electronic Publication Date:||7-Jun-2012|
|Citation:||Chudnovsky, Maria, Oum, Sang-Il, Seymour, Paul. (2012). Finding minimum clique capacity. COMBINATORICA, 32 (283 - 287. doi:10.1007/s00493-012-2891-9|
|Pages:||283 - 287|
|Type of Material:||Journal Article|
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