A generalization of Ramsey theory for linear forests
نویسندگان
چکیده
Chung and Liu defined the d-chromatic Ramsey numbers as a generalization of Ramsey numbers by replacing a weaker condition. Let 1 < d < c and let t = (c d ) . Assume A1, A2, . . . , At are all d-subsets of a set containing c distinct colors. Let G1, G2, . . . , Gt be graphs. The d-chromatic Ramsey number denoted by rc d(G1, G2, . . . , Gt) is defined as the least number p such that, if the edges of the complete graph Kp are colored in any fashion with c colors, then for some i, the subgraph whose edges are colored by colors in Ai contains a Gi. In this paper, we determine rc d(G1, G2, . . . , Gt) where Gi is a linear forest (disjoint union of paths) and d = c− 1 ≤ 3.
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ورودعنوان ژورنال:
- Int. J. Comput. Math.
دوره 89 شماره
صفحات -
تاریخ انتشار 2012