RAIRO-Theor. Inf. Appl.
Volume 39, Number 1, January-March 2005Imre Simon, the tropical computer scientist
|Page(s)||191 - 206|
|Published online||15 March 2005|
A note on the Size-Ramsey number of long subdivisions of graphs
Departamento de Informática, Universidade
Federal do Paraná, Centro Politécnico Caixa Postal 19081, 81531-980
Curitiba PR, Brasil; e-mail:
2 Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada; e-mail:
3 Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, 05508–090 São Paulo SP, Brasil; e-mail:
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.
Mathematics Subject Classification: 05C55 / 05D40
Key words: The Size-Ramsey number / Ramsey theory / expanders / Ramanujan graphs / explicit constructions.
© EDP Sciences, 2005
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