Computation of the vertex Folkman numbers and .
Nedialkov, Evgeni, Nenov, Nedyalko (2002)
The Electronic Journal of Combinatorics [electronic only]
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Displaying similar documents to “On a Class of Vertex Folkman Numbers”
Computation of the vertex Folkman numbers and .
On the 3-Colouring Vertex Folkman Number F(2,2,4)
Nenov, Nedyalko (2001)
Serdica Mathematical Journal
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In this note we prove that F (2, 2, 4) = 13.
Uniquely -colorable and chromatically equivalent graphs.
Chao, Chong-Yun (2001)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Induced complete -partite graphs in dense clique-less graphs.
Fischer, Eldar (1999)
The Electronic Journal of Combinatorics [electronic only]
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Dense -free graphs are almost -partite.
Allen, Peter (2010)
The Electronic Journal of Combinatorics [electronic only]
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New upper bound for a class of vertex Folkman numbers.
Kolev, N., Nenov, N. (2006)
The Electronic Journal of Combinatorics [electronic only]
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Upper and lower bounds for .
Xu, Xiaodong, Luo, Haipeng, Shao, Zehui (2010)
The Electronic Journal of Combinatorics [electronic only]
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Sequences of Maximal Degree Vertices in Graphs
Khadzhiivanov, Nickolay, Nenov, Nedyalko (2004)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 05C35. Let Γ(M ) where M ⊂ V (G) be the set of all vertices of the graph G adjacent to any vertex of M. If v1, . . . , vr is a vertex sequence in G such that Γ(v1, . . . , vr ) = ∅ and vi is a maximal degree vertex in Γ(v1, . . . , vi−1), we prove that e(G) ≤ e(K(p1, . . . , pr)) where K(p1, . . . , pr ) is the complete r-partite graph with pi = |Γ(v1, . . . , vi−1) Γ(vi )|.
On subgraphs induced by transversals in vertex-partitions of graphs.
Axenovich, Maria (2006)
The Electronic Journal of Combinatorics [electronic only]
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The bondage number of graphs: good and bad vertices
Vladimir Samodivkin (2008)
Discussiones Mathematicae Graph Theory
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The domination number γ(G) of a graph G is the minimum number of vertices in a set D such that every vertex of the graph is either in D or is adjacent to a member of D. Any dominating set D of a graph G with |D| = γ(G) is called a γ-set of G. A vertex x of a graph G is called: (i) γ-good if x belongs to some γ-set and (ii) γ-bad if x belongs to no γ-set. The bondage number b(G) of a nonempty graph G is the cardinality of a smallest set of edges whose removal from G results in a graph...
On the Non-(p−1)-Partite Kp-Free Graphs
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?