Highly connected subgraphs of graphs with given independence number
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چکیده
Let G be a graph on n vertices with independence number α. What is the largest k-connected subgraph that G must contain? We prove that if n is sufficiently large (n ≥ αk + 1 will do), then G always contains a k-connected subgraph on at least n/α vertices. This is sharp, since G might be the disjoint union of α equally-sized cliques. For k ≥ 3 and α = 2, 3, we shall prove that the same result holds for n ≥ 4(k − 1) and n ≥ 27(k−1) 4 respectively, and that these lower bounds on n are sharp.
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تاریخ انتشار 2016