An Extension of Turán's Theorem, Uniqueness and Stability
نویسندگان
چکیده
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. Supported by DIMAP, EPSRC award EP/D063191/1, FAPESP (Proc. 2010/09555-7) and grateful to NUMEC/USP, Núcleo de Modelagem Estocástica e Complexidade of the University of São Paulo, for supporting this research. Supported by FAPESP (Proc. 2009/17831-7) and grateful to NUMEC/USP, Núcleo de Modelagem Estocástica e Complexidade of the University of São Paulo, for supporting this research. Supported by DIMAP, EPSRC award EP/D063191/1. The work was done while the author was an EPSRC Fellow at the Mathematics Institute, University of Warwick, UK. Supported by DIMAP, EPSRC award EP/D063191/1. The research leading to this result has received funding from the European Union’s Seventh Framework Programme (FP7/2007-2013) under grant agreement no. PIEF-GA-2009-253925. the electronic journal of combinatorics 21(4) (2014), #P4.5 1
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عنوان ژورنال:
- Electr. J. Comb.
دوره 21 شماره
صفحات -
تاریخ انتشار 2014