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

Jair Donadelli; Penny E. Haxell; Yoshiharu Kohayakawa

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2005)

- Volume: 39, Issue: 1, page 191-206
- ISSN: 0988-3754

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topDonadelli, Jair, Haxell, Penny E., and Kohayakawa, Yoshiharu. "A note on the Size-Ramsey number of long subdivisions of graphs." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 39.1 (2005): 191-206. <http://eudml.org/doc/245047>.

@article{Donadelli2005,

abstract = {Let $T_sH$ 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 $T_sH$.},

author = {Donadelli, Jair, Haxell, Penny E., Kohayakawa, Yoshiharu},

journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},

keywords = {The Size-Ramsey number; Ramsey theory; expanders; Ramanujan graphs; explicit constructions},

language = {eng},

number = {1},

pages = {191-206},

publisher = {EDP-Sciences},

title = {A note on the Size-Ramsey number of long subdivisions of graphs},

url = {http://eudml.org/doc/245047},

volume = {39},

year = {2005},

}

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

PB - EDP-Sciences

VL - 39

IS - 1

SP - 191

EP - 206

AB - Let $T_sH$ 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 $T_sH$.

LA - eng

KW - The Size-Ramsey number; Ramsey theory; expanders; Ramanujan graphs; explicit constructions

UR - http://eudml.org/doc/245047

ER -

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