Displaying similar documents to “Multicolor Ramsey numbers for some paths and cycles”

The Ramsey number r(C₇,C₇,C₇)

Ralph Faudree, Annette Schelten, Ingo Schiermeyer (2003)

Discussiones Mathematicae Graph Theory

Similarity:

Bondy and Erdős [2] have conjectured that the Ramsey number for three cycles Cₖ of odd length has value r(Cₖ,Cₖ,Cₖ) = 4k-3. We give a proof that r(C₇,C₇,C₇) = 25 without using any computer support.

The exit path of a Markov chain with rare transitions

Olivier Catoni, Raphaël Cerf (2010)

ESAIM: Probability and Statistics

Similarity:

We study the exit path from a general domain after the last visit to a set of a Markov chain with rare transitions. We prove several large deviation principles for the law of the succession of the cycles visited by the process (the cycle path), the succession of the saddle points gone through to jump from cycle to cycle on the cycle path (the saddle path) and the succession of all the points gone through (the exit path). We estimate the time the process spends in each cycle of...

Minimal cycle bases of the lexicographic product of graphs

M.M.M. Jaradat (2008)

Discussiones Mathematicae Graph Theory

Similarity:

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.