Geodesic
An extension of Turán's theorem, uniqueness and stability
Peter Allen1 ; Julia Böttcher1 ; Jan Hladký2 ; Diana Piguet3
1London School of Economics and Political Sciences
2Czech Academy of Sciences
3University of West Bohemia
The electronic journal of combinatorics, Tome 21 (2014) no. 4
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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 $M\subset V(G)$. For $(r-1)|M|\ge n$, the $(r-1)$-partite Turán graph turns out to be the unique extremal graph. For $(r-1)|M|, there is a whole family of extremal graphs, which we describe explicitly. In addition we provide corresponding stability results.
DOI : 10.37236/4194
Classification : 05C35
Mots-clés : graph theory, Turan's theorem

Peter Allen  1   ; Julia Böttcher  1   ; Jan Hladký  2   ; Diana Piguet  3

1 London School of Economics and Political Sciences
2 Czech Academy of Sciences
3 University of West Bohemia 
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     title = {An extension of {Tur\'an's} theorem, uniqueness and stability},
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     doi = {10.37236/4194},
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     url = {http://geodesic.mathdoc.fr/articles/10.37236/4194/}
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Peter Allen; Julia Böttcher; Jan Hladký; Diana Piguet. An extension of Turán's theorem, uniqueness and stability. The electronic journal of combinatorics, Tome 21 (2014) no. 4. doi: 10.37236/4194

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