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Article Dans Une Revue SIAM Journal on Discrete Mathematics Année : 2016

Isolating Highly Connected Induced Subgraphs

Résumé

We prove that any graph $G$ of minimum degree greater than $2k^2-1$ has a $(k+1)$-connected induced subgraph $H$ such that the number of vertices of $H$ that have neighbors outside of $H$ is at most $2k^2-1$. This generalizes a classical result of Mader, which states that a high minimum degree implies the existence of a highly connected subgraph. We give several variants of our result, and for each of these variants, we give asymptotics for the bounds. We also compute optimal values for the case when $k=2$. Alon, Kleitman, Saks, Seymour, and Thomassen proved that in a graph of high chromatic number, there exists an induced subgraph of high connectivity and high chromatic number. We give a new proof of this theorem with a better bound.

Dates et versions

hal-01324067 , version 1 (31-05-2016)

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Citer

Irena Penev, Stéphan Thomassé, Nicolas Trotignon. Isolating Highly Connected Induced Subgraphs. SIAM Journal on Discrete Mathematics, 2016, 30, pp.592-619. ⟨10.1137/140981939⟩. ⟨hal-01324067⟩
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