Let be the graph obtained from a given graph by subdividing each edge 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 , there exist graphs with edges that are Ramsey with respect to .
Mots clés : The Size-Ramsey number, Ramsey theory, expanders, Ramanujan graphs, explicit constructions
@article{ITA_2005__39_1_191_0, author = {Donadelli, Jair and Haxell, Penny E. and Kohayakawa, Yoshiharu}, title = {A note on the {Size-Ramsey} number of long subdivisions of graphs}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, pages = {191--206}, publisher = {EDP-Sciences}, volume = {39}, number = {1}, year = {2005}, doi = {10.1051/ita:2005019}, mrnumber = {2132587}, zbl = {1075.05054}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ita:2005019/} }
TY - JOUR AU - Donadelli, Jair AU - Haxell, Penny E. AU - Kohayakawa, Yoshiharu TI - A note on the Size-Ramsey number of long subdivisions of graphs JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2005 SP - 191 EP - 206 VL - 39 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ita:2005019/ DO - 10.1051/ita:2005019 LA - en ID - ITA_2005__39_1_191_0 ER -
%0 Journal Article %A Donadelli, Jair %A Haxell, Penny E. %A Kohayakawa, Yoshiharu %T A note on the Size-Ramsey number of long subdivisions of graphs %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2005 %P 191-206 %V 39 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ita:2005019/ %R 10.1051/ita:2005019 %G en %F ITA_2005__39_1_191_0
Donadelli, Jair; Haxell, Penny E.; Kohayakawa, Yoshiharu. A note on the Size-Ramsey number of long subdivisions of graphs. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005) no. 1, pp. 191-206. doi : 10.1051/ita:2005019. http://archive.numdam.org/articles/10.1051/ita:2005019/
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