Computation of the vertex Folkman numbers and .
Nedialkov, Evgeni, Nenov, Nedyalko (2002)
The Electronic Journal of Combinatorics [electronic only]
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Nedialkov, Evgeni, Nenov, Nedyalko (2002)
The Electronic Journal of Combinatorics [electronic only]
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Wood, Rupert G., Woodall, Douglas R. (2009)
The Electronic Journal of Combinatorics [electronic only]
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Alon, Noga, Sudakov, Benny (2006)
The Electronic Journal of Combinatorics [electronic only]
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Chao, Chong-Yun (2001)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Allen, Peter (2010)
The Electronic Journal of Combinatorics [electronic only]
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Kinnari Amin, Jill Faudree, Ronald J. Gould, Elżbieta Sidorowicz (2013)
Discussiones Mathematicae Graph Theory
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We say that a graph G is maximal Kp-free if G does not contain Kp but if we add any new edge e ∈ E(G) to G, then the graph G + e contains Kp. We study the minimum and maximum size of non-(p − 1)-partite maximal Kp-free graphs with n vertices. We also answer the interpolation question: for which values of n and m are there any n-vertex maximal Kp-free graphs of size m?
Nenov, Nedyalko (2002)
Serdica Mathematical Journal
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Let a1 , . . . , ar, be positive integers, i=1 ... r, m = ∑(ai − 1) + 1 and p = max{a1 , . . . , ar }. For a graph G the symbol G → (a1 , . . . , ar ) means that in every r-coloring of the vertices of G there exists a monochromatic ai -clique of color i for some i ∈ {1, . . . , r}. In this paper we consider the vertex Folkman numbers F (a1 , . . . , ar ; m − 1) = min |V (G)| : G → (a1 , . . . , ar ) and Km−1 ⊂ G} We prove that F (a1 , . . . , ar ; m − 1) = m + 6, if p = 3 and m ≧ 6...
Axenovich, Maria (2006)
The Electronic Journal of Combinatorics [electronic only]
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Xu, Xiaodong, Luo, Haipeng, Shao, Zehui (2010)
The Electronic Journal of Combinatorics [electronic only]
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Caro, Yair, Yuster, Raphael (2003)
The Electronic Journal of Combinatorics [electronic only]
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Fischer, Eldar (1999)
The Electronic Journal of Combinatorics [electronic only]
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Sebastian Urbański (1996)
Discussiones Mathematicae Graph Theory
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The paper gives an account of previous and recent attempts to determine the order of a smallest graph not containing K₅ and such that every 2-coloring of its edges results in a monochromatic triangle. A new 14-vertex K₄-free graph with the same Ramsey property in the vertex coloring case is found. This yields a new construction of one of the only two known 15-vertex (3,3)-Ramsey graphs not containing K₅.
Axenovich, Maria, Martin, Ryan (2008)
The Electronic Journal of Combinatorics [electronic only]
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