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

Donadelli, Jair; Haxell, Penny E.; Kohayakawa, Yoshiharu

doi:10.1051/ita:2005019

Geodesic

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

Donadelli, Jair ; Haxell, Penny E. ; Kohayakawa, Yoshiharu

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005) no. 1, pp. 191-206

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Résumé

Let $T_{s} H$ 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 $T_{s} H$ .

MR Zbl

DOI : 10.1051/ita:2005019

Classification : 05C55, 05D40
Keywords: The Size-Ramsey number, Ramsey theory, expanders, Ramanujan graphs, explicit constructions

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     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://geodesic.mathdoc.fr/articles/10.1051/ita:2005019/}
}

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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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