Author:
KEEVASH PETER,LOCHET WILLIAM
Abstract
The (a,b)-eye is the graph Ia,b = Ka+b \ Kb obtained by deleting the edges of a clique of size b from a clique of size a+b. We show that for any a,b ≥ 2 and p ∈ (0,1), if we condition the random graph G ~ G(n,p) on having no induced copy of Ia,b, then with high probability G is close to an a-partite graph or the complement of a (b−1)-partite graph. Our proof uses the recently developed theory of hypergraph containers, and a stability result for an extremal problem with two weighted colours. We also apply the stability method to obtain an exact Turán-type result for this extremal problem.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science
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