Ramsey Numbers of Trees Versus Multiple Copies of Books  

作　　者：Xiao-bing GUO Si-nan HU Yue-jian PENG 

机构地区：[1]School of Mathematical Sciences,Luoyang Normal University,Luoyang 471934,China [2]School of Mathematics,Hunan University,Changsha 410082,China

出　　处：《Acta Mathematicae Applicatae Sinica》2024年第3期600-612,共13页应用数学学报（英文版）

基　　金：supported in part by National Natural Science Foundation of China (No.11931002);China Postdoctoral Science Foundation (No.2021M701162)。

摘　　要：Given two graphs G and H,the Ramsey number R(G,H) is the minimum integer N such that any two-coloring of the edges of K_(N) in red or blue yields a red G or a blue H.Let v(G) be the number of vertices of G and χ(G) be the chromatic number of G.Let s(G) denote the chromatic surplus of G,the number of vertices in a minimum color class among all proper χ(G)-colorings of G.Burr showed that R(G,H)≥(v(G)-1)(χ(H)-1)+s(H) if G is connected and v(G)≥s(H).A connected graph G is H-good if R(G,H)=(v(G)-1)(χ(H)-1)+s(H).Let tH denote the disjoint union of t copies of graph H,and let G∨H denote the join of G and H.Denote a complete graph on n vertices by K_(n),and a tree on n vertices by T_(n).Denote a book with n pages by B_(n),i.e.,the join K_(2) ∨■.Erd?s,Faudree,Rousseau and Schelp proved that T_(n) is B_(m)-good if n≥3m-3.In this paper,we obtain the exact Ramsey number of T_(n) versus 2B_(2).Our result implies that T_(n) is 2B_(2)-good if n≥5.

关 键 词：ramsey number ramsey goodness TREE BOOK 

分 类 号：O157.5[理学—数学]