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arXiv · 1403.3801

An extension of Turán's Theorem, uniqueness and stability

Peter Allen·Julia Böttcher·Jan Hladký·Diana Piguet
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Abstract

We determine the maximum number of edges of an $n$-vertex graph $G$ with the property that none of its $r$-cliques intersects a fixed set $M\subset V(G)$. For $(r-1)|M|\ge n$, the $(r-1)$-partite Turan graph turns out to be the unique extremal graph. For $(r-1)|M|<n$, there is a whole family of extremal graphs, which we describe explicitly. In addition we provide corresponding stability results.

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Peter Allen, Julia Böttcher, Jan Hladký, Diana Piguet. 2014-08-01. An extension of Turán's Theorem, uniqueness and stability. https://arxiv.org/abs/1403.3801

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