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Article Dans Une Revue The Electronic Journal of Combinatorics Année : 2020

On Fractional Fragility Rates of Graph Classes

Sur les taux de fragilité fractionnaire des classes de graphes

Résumé

We consider, for every positive integer a, probability distributions on subsets of vertices of a graph with the property that every vertex belongs to the random set sampled from this distribution with probability at most 1/a. Among other results, we prove that for every positive integer a and every planar graph G, there exists such a probability distribution with the additional property that for any set X in the support of the distribution, the graph G − X has component-size at most (∆(G) − 1) a+O(√ a) , or treedepth at most O(a 3 log 2 (a)). We also provide nearly-matching lower bounds.
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Dates et versions

hal-03044090 , version 1 (07-12-2020)

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Citer

Zdeněk Dvořák, Jean-Sébastien Sereni. On Fractional Fragility Rates of Graph Classes. The Electronic Journal of Combinatorics, 2020, 27 (4), ⟨10.37236/8909⟩. ⟨hal-03044090⟩
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