A note on the Size-Ramsey number of long subdivisions of graphs
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 39 (2005) no. 1, p. 191-206

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.

DOI : https://doi.org/10.1051/ita:2005019
Classification:  05C55,  05D40
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},
     publisher = {EDP-Sciences},
     volume = {39},
     number = {1},
     year = {2005},
     pages = {191-206},
     doi = {10.1051/ita:2005019},
     zbl = {1075.05054},
     mrnumber = {2132587},
     language = {en},
     url = {http://www.numdam.org/item/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, Volume 39 (2005) no. 1, pp. 191-206. doi : 10.1051/ita:2005019. http://www.numdam.org/item/ITA_2005__39_1_191_0/

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