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Bounding the vertex cover number of a hypergraph

✍ Scribed by Guo-Li Ding; Paul Seymour; Peter Winkler

Publisher
Springer-Verlag
Year
1994
Tongue
English
Weight
539 KB
Volume
14
Category
Article
ISSN
0209-9683

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πŸ“œ SIMILAR VOLUMES

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We present a lower bound on the independence number of arbitrary hypergraphs in terms of the degree vectors. The degree vector of a vertex v is given by d is the number of edges of size m containing v. We define a function f with the property that any hypergraph H = (V, E) satisfies Ξ±(H) β‰₯ v∈V f (d

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Burr recently proved [3] that for positive integers m , , m 2 , . . , , m, and any graph G we have x(G) 5 &, if and only if G can be expressed as the edge disjoint union of subgraphs F, satisfying x(F,) 5 m,. This theorem is generalized to hypergraphs. By suitable interpretations the generalization

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## This note generalizes the notion of cyclomatic number (or cycle rank) from Graph Theory to Hypergraph Theory and links it up with the concept of planarity in hypergraphs which was recently introducea by R.P. Jones. Sharp bounds are obtained for the cyclomatic number of the planar hypergraphs an