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10

CORR
2010
Springer

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The overlap number of a graph

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The overlap number of a graph

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An overlap representation is an assignment of sets to the vertices of a graph in such a way that two vertices are adjacent if and only if the sets assigned to them overlap. The overlap number of a graph is the minimum number of elements needed to form such a representation. We find the overlap numbers of cliques and complete bipartite graphs by relating the problem to previous research in combinatorics. The overlap numbers of paths, cycles, and caterpillars are also established. Finally, we show the NP-completeness of the problems of extending an overlap representation and finding a minimum overlap representation with limited containment.

Bill Rosgen, Lorna Stewart

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CORR 2010 | Education | Minimum Number | Overlap Numbers | Overlap Representation |

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Added	09 Dec 2010
Updated	09 Dec 2010
Type	Journal
Year	2010
Where	CORR
Authors	Bill Rosgen, Lorna Stewart

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