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Upper Bounds to the Number of Vertices in a k-Critically n-Connected Graph

Research paper by Matthias Kriesell

Indexed on: 01 Mar '02Published on: 01 Mar '02Published in: Graphs and Combinatorics



Abstract

 Let k≤n be positive integers. A finite, simple, undirected graph is called k-critically n-connected, or, briefly, an (n,k)-graph, if it is noncomplete and n-connected and the removal of any set X of at most k vertices results in a graph which is not (n−|X|+1)-connected. We present some new results on the number of vertices of an (n,k)-graph, depending on new estimations of the transversal number of a uniform hypergraph with a large independent edge set.