Maximal degrees in subgraphs of Kneser graphs

04/18/2020

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by   Peter Frankl, et al.

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In this paper, we study the maximum degree in non-empty induced subgraphs of the Kneser graph KG(n,k). One of the main results asserts that, for k>k_0 and n>64k^2, whenever a non-empty subgraph has m≥ kn-2 k-2 vertices, its maximum degree is at least 1/2(1-k^2/n) m - n-2 k-2≥ 0.49 m. This bound is essentially best possible. One of the intermediate steps is to obtain structural results on non-empty subgraphs with small maximum degree.