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

Jair Donadelli; Penny E. Haxell; Yoshiharu Kohayakawa — 2005

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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 $T_{s} H$ .

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

Jair Donadelli; Penny E. Haxell; Yoshiharu Kohayakawa — 2010

RAIRO - Theoretical Informatics and Applications

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 (SODA 2002) 321–328], we prove that, for any graph , there exist graphs with edges that are Ramsey with respect to .

A density result for random sparse oriented graphs and its relation to a conjecture of Woodall.

Donadelli, Jair; Kohayakawa, Yoshiharu — 2002

The Electronic Journal of Combinatorics [electronic only]

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Currently displaying 1 – 3 of 3

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

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

A density result for random sparse oriented graphs and its relation to a conjecture of Woodall.