An extension of Turán's theorem, uniqueness and stability

Allen, Peter, Böttcher, Julia, Hladký, Jan and Piguet, Diana (2014) An extension of Turán's theorem, uniqueness and stability. Electronic Journal of Combinatorics, 21 (4). P4.5. ISSN 1077-8926

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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⊂V(G) . For (r−1)|M|≥n , the (r−1) -partite Turán 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.

Item Type:	Article
Official URL:	http://www.combinatorics.org/ojs/index.php/eljc/in...
Additional Information:	© 2014 The Authors
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Sets:	Departments > Mathematics
Date Deposited:	24 Nov 2014 10:15
Last Modified:	20 Jan 2020 05:31
Projects:	EP/D063191/1, FAPESP (Proc. 2010/09555-7), PIEF-GA-2009-253925
Funders:	DIMAP, EPSRC, European Union’s Seventh Framework Programme (FP7/2007-2013)
URI:	http://eprints.lse.ac.uk/id/eprint/60232

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