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Multicolor Ramsey numbers for paths and cycles

Tomasz Dzido (2005)

Discussiones Mathematicae Graph Theory

For given graphs G₁,G₂,...,Gₖ, k ≥ 2, the multicolor Ramsey number R(G₁,G₂,...,Gₖ) is the smallest integer n such that if we arbitrarily color the edges of the complete graph on n vertices with k colors, then it is always a monochromatic copy of some G i , for 1 ≤ i ≤ k. We give a lower bound for k-color Ramsey number R(Cₘ,Cₘ,...,Cₘ), where m ≥ 8 is even and Cₘ is the cycle on m vertices. In addition, we provide exact values for Ramsey numbers R(P₃,Cₘ,Cₚ), where P₃ is the path on 3 vertices, and several...

Multicolor Ramsey numbers for some paths and cycles

Halina Bielak (2009)

Discussiones Mathematicae Graph Theory

We give the multicolor Ramsey number for some graphs with a path or a cycle in the given sequence, generalizing a results of Faudree and Schelp [4], and Dzido, Kubale and Piwakowski [2,3].

Multi-faithful spanning trees of infinite graphs

Norbert Polat (2001)

Czechoslovak Mathematical Journal

For an end τ and a tree T of a graph G we denote respectively by m ( τ ) and m T ( τ ) the maximum numbers of pairwise disjoint rays of G and T belonging to τ , and we define t m ( τ ) : = min { m T ( τ ) T is a spanning tree of G } . In this paper we give partial answers—affirmative and negative ones—to the general problem of determining if, for a function f mapping every end τ of G to a cardinal f ( τ ) such that t m ( τ ) ≤ f ( τ ) ≤ m ( τ ) , there exists a spanning tree T of G such that m T ( τ ) = f ( τ ) for every end τ of G .

Multiples of left loops and vertex-transitive graphs

Eric Mwambene (2005)

Open Mathematics

Via representation of vertex-transitive graphs on groupoids, we show that left loops with units are factors of groups, i.e., left loops are transversals of left cosets on which it is possible to define a binary operation which allows left cancellation.

Currently displaying 261 – 280 of 294