科研之友
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摘要
The size-Ramsey number (R) over cap (T, H) of a family of graphs and a graph H is the smallest integer m such that there exists a graph G on m edges with the property that any coloring of the edges of G with two colors, say, red and blue, yields a red copy of a graph from.F or a blue copy of H. In this paper we first focus on F = C-<= cn, where C-<= cn, is the family of cycles of length at most en, and H = P-n. In particular, we show that 2.00365n <= (R) over cap (C-<= n, P-n) <= 31n. Using similar techniques, we also managed to analyze (R) over cap (C-n, Pn, which was investigated before but until last year only by using the regularity method.
- 出版日期2018-7
