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 .
Keywords: 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},
year = {2005},
publisher = {EDP Sciences},
volume = {39},
number = {1},
doi = {10.1051/ita:2005019},
mrnumber = {2132587},
zbl = {1075.05054},
language = {en},
url = {https://www.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 - https://www.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 https://www.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
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