论文信息 - Ramsey and 2-local Ramsey numbers for disjoint unions of cycles

Ramsey and 2-local Ramsey numbers for disjoint unions of cycles

We prove an upper bound for the Ramsey number of the disjoint union of odd cycles generalizing a result of Denley [The Ramsey numbers for disjoint unions of cycles, Discrete Math. 149 (1996) 31-44]. Moreover, we study the relation between the 2-local Ramsey number R"2"-"l"o"c(G) and the Ramsey number R(G), where G is a disjoint union of odd cycles. We give the exact value of the 2-local Ramsey number in the case when each cycle of G has an odd order.

Halina Bielak

[1] Zsolt Tuza,et al. Linear upper bounds for local Ramsey numbers , 1987, Graphs Comb..

[2] Zsolt Tuza,et al. Ramsey numbers for local colorings , 1987, Graphs Comb..

[3] Miroslaw Truszczynski,et al. A note on local colorings of graphs , 1997, Discret. Math..

[4] Iwao Sato,et al. Ramsey numbers for unions of some cycles , 1988, Discret. Math..

[5] Miroslaw Truszczynski. Generalized local colorings of graphs , 1992, J. Comb. Theory, Ser. B.

[6] Halina Bielak. Local Ramsey numbers for some graphs , 2003, Discret. Math..

[7] Richard H. Schelp,et al. All Ramsey numbers for cycles in graphs , 1974, Discret. Math..

[8] Vojtech Rödl,et al. Local k-colorings of graphs and hypergraphs , 1987, J. Comb. Theory, Ser. B.

[9] Tristan Denley. The Ramsey numbers for disjoint unions of cycles , 1996, Discret. Math..

[10] Zsolt Tuza,et al. On k-local and k-mean colorings of graphs and hypergraphs , 1993 .

[11] Halina Bielak. Local Ramsey numbers for copies of cycles , 2004, Discret. Math..

[12] P. Erdös,et al. Ramsey Numbers for Cycles in Graphs , 1973 .

[13] Joel Spencer,et al. Ramsey theorems for multiple copies of graphs , 1975 .