Displaying similar documents to “The Ramsey number r(C₇,C₇,C₇)”

Multicolor Ramsey numbers for some paths and cycles

Halina Bielak (2009)

Discussiones Mathematicae Graph Theory

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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].

Cycles in graphs and related problems

Antoni Marczyk

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Our aim is to survey results in graph theory centered around four themes: hamiltonian graphs, pancyclic graphs, cycles through vertices and the cycle structure in a graph. We focus on problems related to the closure result of Bondy and Chvátal, which is a common generalization of two fundamental theorems due to Dirac and Ore. We also describe a number of proof techniques in this domain. Aside from the closure operation we give some applications of Ramsey theory in the research of cycle...

Minimal cycle bases of the lexicographic product of graphs

M.M.M. Jaradat (2008)

Discussiones Mathematicae Graph Theory

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A construction of minimum cycle bases of the lexicographic product of graphs is presented. Moreover, the length of a longest cycle of a minimal cycle basis is determined.

A note on total colorings of planar graphs without 4-cycles

Ping Wang, Jian-Liang Wu (2004)

Discussiones Mathematicae Graph Theory

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Let G be a 2-connected planar graph with maximum degree Δ such that G has no cycle of length from 4 to k, where k ≥ 4. Then the total chromatic number of G is Δ +1 if (Δ,k) ∈ {(7,4),(6,5),(5,7),(4,14)}.

The cycle-complete graph Ramsey number r(C₅,K₇)

Ingo Schiermeyer (2005)

Discussiones Mathematicae Graph Theory

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The cycle-complete graph Ramsey number r(Cₘ,Kₙ) is the smallest integer N such that every graph G of order N contains a cycle Cₘ on m vertices or has independence number α(G) ≥ n. It has been conjectured by Erdős, Faudree, Rousseau and Schelp that r(Cₘ,Kₙ) = (m-1)(n-1)+1 for all m ≥ n ≥ 3 (except r(C₃,K₃) = 6). This conjecture holds for 3 ≤ n ≤ 6. In this paper we will present a proof for r(C₅,K₇) = 25.

Some crossing numbers of products of cycles

Marián Klešč (2005)

Discussiones Mathematicae Graph Theory

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The exact values of crossing numbers of the Cartesian products of four special graphs of order five with cycles are given and, in addition, all known crossing numbers of Cartesian products of cycles with connected graphs on five vertices are summarized.