Displaying similar documents to “Notes on nonrepetitive graph colouring.”

Weak Saturation Numbers for Sparse Graphs

Ralph J. Faudree, Ronald J. Gould, Michael S. Jacobson (2013)

Discussiones Mathematicae Graph Theory


For a fixed graph F, a graph G is F-saturated if there is no copy of F in G, but for any edge e ∉ G, there is a copy of F in G + e. The minimum number of edges in an F-saturated graph of order n will be denoted by sat(n, F). A graph G is weakly F-saturated if there is an ordering of the missing edges of G so that if they are added one at a time, each edge added creates a new copy of F. The minimum size of a weakly F-saturated graph G of order n will be denoted by wsat(n, F). The graphs...

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 .

Fruit salad.

Gyárfás, András (1997)

The Electronic Journal of Combinatorics [electronic only]