Size Ramsey Numbers of Star Forests

• Main Authors: Yen-Jen Cheng, 鄭硯仁
• Other Authors: Gerard Jennhwa Chang
• Format: Others
• Language: en_US
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/90037993628306039321

碩士 === 國立臺灣大學 === 數學研究所 === 98 === For graphs G_1, G_2, ..., G_r and F, we write F -> (G_1, G_2, ..., G_r)$ to mean that if the edges of F are colored by 1, 2, ..., r then there exists some i such that the edges of color i contains a copy of G_i. The size Ramsey number r(G_1, G_2, ..., G_r) is the least number of edges of a graph F for which F -> (G_1, G_2, ..., G_r). Suppose G_1 = U_{i=1}^{m}{K_{1,a_i}} with a_1 >= a_2 >= ... >= a_m and G_2 = U_{i=1}^{n}{K_{1, b_i}} with b_1 >= b_2 >= ... >= b_n. Let l_s = max_{i+j=s+1}{(a_i+b_j-1)}. Burr, Erdos, Faudree, Rousseau and Schelp [4] conjectured that r(G_1, G_2) = sum_{s=1}^{m+n-1}{ell_s}. The purpose of this thesis is to study the conjecture for the case when a_i = b_j = 1 for 2 <= i <= m and $2 <= j <= n.