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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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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:
Additional Information: © 2014 The Authors
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 24 Nov 2014 10:15
Last Modified: 16 May 2024 01:55
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)

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