Chromatic Vertex Folkman Numbers
نویسندگان
چکیده
منابع مشابه
Chromatic Vertex Folkman Numbers
For graph G and integers a1 ≥ · · · ≥ ar ≥ 2, we write G → (a1, · · · , ar) if and only if for every r-coloring of the vertex set V (G) there exists a monochromatic Kai in G for some color i ∈ {1, · · · , r}. The vertex Folkman number Fv(a1, · · · , ar; s) is defined as the smallest integer n for which there exists a Ks-free graph G of order n such that G→ (a1, · · · , ar). It is well known tha...
متن کاملOn the Vertex Folkman Numbers
For a graph G the symbol G v −→ (a1, . . . , ar) means that in every r-coloring of the vertices of G, for some i ∈ {1, 2, . . . , r}, there exists a monochromatic ai-clique of color i. The vertex Folkman numbers Fv(a1, . . . , ar; q) = min{|V (G)| : G v −→ (a1, . . . , ar) and Kq * G} are considered. We prove that Fv(2, . . . , 2 | {z } r ; r − 1) = r + 7, r ≥ 6 and Fv(2, . . . , 2 | {z } r ; r...
متن کاملNew Upper Bound on Vertex Folkman Numbers
In 1970, J. Folkman proved that for a given integer r and a graph G of order n there exists a graph H with the same clique number as G such that every r coloring of vertices of H yields at least one monochromatic copy of G. His proof gives no good bound on the order of graph H, i.e. the order of H is bounded by an iterated power function. A related problem was studied by Luczak, Ruciński and Ur...
متن کاملComputation of the vertex Folkman numbers
In this note we show that the exact value of the vertex Folkman numbers F (2, 2, 2, 4; 6) and F (2, 3, 4; 6) is 14.
متن کاملSome remarks on vertex Folkman numbers for hypergraphs
Let F (r,G) be the least order of H such that the clique number of H and G are equal and any r-coloring of the vertices of H yields a monochromatic and induced copy of G. The problem of bounding of F (r,G) was studied by several authors and it is well understood. In this note, we extend those results to uniform hypergraphs.
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2020
ISSN: 1077-8926
DOI: 10.37236/7862