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A note on the Size-Ramsey number of long subdivisions of graphs

Published online by Cambridge University Press:  15 March 2005

Jair Donadelli ,
Penny E. Haxell  and
Yoshiharu Kohayakawa
Jair Donadelli
Affiliation:
Departamento de Informática, Universidade Federal do Paraná, Centro Politécnico Caixa Postal 19081, 81531-980 Curitiba PR, Brasil; e-mail: 
Penny E. Haxell
Affiliation:
Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada; e-mail: 
Yoshiharu Kohayakawa
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, 05508–090 São Paulo SP, Brasil; e-mail: 
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Abstract

Let TsH be the graph obtained from a given graph H by subdividing each edge s times. Motivated by a problem raised by Igor Pak [Mixing time and long paths in graphs, in Proc. of the 13th annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2002) 321–328], we prove that, for any graph H, there exist graphs G with O(s) edges that are Ramsey with respect to TsH.

Keywords

The Size-Ramsey numberRamsey theoryexpandersRamanujan graphsexplicit constructions.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 39 , Issue 1: Imre Simon, the tropical computer scientist , January 2005 , pp. 191 - 206
Copyright
© EDP Sciences, 2005

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