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On a Class of Vertex Folkman Numbers

Nenov, Nedyalko — 2002

Serdica Mathematical Journal

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 (Theorem 3)...

On the 3-Colouring Vertex Folkman Number F(2,2,4)

Nenov, Nedyalko — 2001

Serdica Mathematical Journal

In this note we prove that F (2, 2, 4) = 13.

On the Vertex Folkman Numbers Fv(2,...,2;q)

Nenov, Nedyalko — 2009

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 05C55. In this paper we shall compute the Folkman numbers ... We prove also new bounds for some vertex and edge Folkman numbers.

Sequences of Maximal Degree Vertices in Graphs

Khadzhiivanov, Nickolay; Nenov, Nedyalko — 2004

Serdica Mathematical Journal

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 )|.

Computation of the vertex Folkman numbers $F (2, 2, 2, 4; 6)$ and $F (2, 3, 4; 6)$ .

Nedialkov, Evgeni; Nenov, Nedyalko — 2002

The Electronic Journal of Combinatorics [electronic only]

An Inequality for Generalized Chromatic Graphs Едно неравенство за обобщени хроматични графи

Bojilov, Asen; Nenov, Nedyalko — 2012

Union of Bulgarian Mathematicians

Асен Божилов, Недялко Ненов - Нека G е n-върхов граф и редицата от степените на върховете му е d1, d2, . . . , dn, а V(G) е множеството от върховете на G. Степента на върха v бележим с d(v). Най-малкото естествено число r, за което V(G) има r-разлагане V(G) = V1 ∪ V2 ∪ · · · ∪ Vr, Vi ∩ Vj = ∅, , i 6 = j такова, че d(v) ≤ n − |Vi|, ∀v ∈ Vi, i = 1, 2, . . . , r е означено с ϕ(G). В тази работа доказваме неравенството ... Let G be a simple n-vertex graph with degree sequence d1, d2, . ....

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Currently displaying 1 – 6 of 6

On a Class of Vertex Folkman Numbers

On the 3-Colouring Vertex Folkman Number F(2,2,4)

On the Vertex Folkman Numbers Fv(2,...,2;q)

Sequences of Maximal Degree Vertices in Graphs

Computation of the vertex Folkman numbers $F (2, 2, 2, 4; 6)$ and $F (2, 3, 4; 6)$ .

An Inequality for Generalized Chromatic Graphs Едно неравенство за обобщени хроматични графи

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Formula preview

Currently displaying 1 – 6 of 6

On a Class of Vertex Folkman Numbers

On the 3-Colouring Vertex Folkman Number F(2,2,4)

On the Vertex Folkman Numbers Fv(2,...,2;q)

Sequences of Maximal Degree Vertices in Graphs

Computation of the vertex Folkman numbers F ( 2 , 2 , 2 , 4 ; 6 ) and F ( 2 , 3 , 4 ; 6 ) .

An Inequality for Generalized Chromatic Graphs Едно неравенство за обобщени хроматични графи

Computation of the vertex Folkman numbers $F (2, 2, 2, 4; 6)$ and $F (2, 3, 4; 6)$ .