The minimum number of e-vertex-covers among hypergraphs with e edges of given ranks

Authors:
F. H. Chang;H. L. Fu;F. K. Hwang;B. C. Lin
Affiliations:
Department of Applied Mathematics, National Chiayi University, Chiayi City, 60004, Taiwan;Department of Applied Mathematics, National Chiao Tung University, Hsinchu, 30050, Taiwan;Department of Applied Mathematics, National Chiao Tung University, Hsinchu, 30050, Taiwan;Department of Math, National Central University, Chung-Li, 32054, Taiwan
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

We study the problem that among all hypergraphs with e edges of ranks l"1,...,l"e and v vertices, which hypergraph has the least number of vertex-covers of size e. The problem is very difficult and we only get some partial answers. We show an application of our results to improve the error-tolerance of a pooling design proposed in the literature.