An extension of Turán's theorem, uniqueness and stability

Allen, Peter ORCID: 0000-0001-6555-3501, Böttcher, Julia ORCID: 0000-0002-4104-3635, 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
Date Deposited:	24 Nov 2014 10:15
Last Modified:	01 Oct 2024 03:41
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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