Star-quadrilateral Ramsey Number and Beyond  

星对四边形的Ramsey数及相关问题

作　　者：CHEN Yaojun ZHANG Xuemei ZHANG Yanbo 陈耀俊;张雪梅;张闫博(南京大学数学学院,江苏南京210093;浙江师范大学数学科学学院,浙江金华321004;河北师范大学数学科学学院,河北石家庄050024)

机构地区：[1]School of Mathematics,Nanjing University,Nanjing,Jiangsu,210093,P.R.China [2]School of Mathematical Sciences,Zhejiang Normal University,Jinhua,Zhejiang,321004,P.R.China [3]School of Mathematical Sciences,Hebei Normal University,Shijiazhuang,Hebei,050024,P.R.China

出　　处：《数学进展》2025年第2期292-314,共23页Advances in Mathematics(China)

基　　金：supported by NSFC(Nos.12161141003,11931006);supported by NSFC(Nos.11801520,12171436,12271489);supported by NSFC(No.11601527)。

摘　　要：For k given graphs H_1,...,H_k with k≥2,the k-color Ramsey number R(H_(1),...,H_(k)) represents the minimum integer N with the following property:if the edges of the complete graph K_(N) are colored with k colors,then there exists some i with 1≤i≤k such that K_N has a subgraph in color i isomorphic to H_(i).Let C_(m) be a cycle of length m and K_(1,n) a star of order n+1.In this paper,we systematically introduce the latest research progress on star-quadrilateral Ramsey numbers and provide an overview of Ramsey numbers concerning quadrilaterals,including multicolor cases.对于给定的k个图H_(1),...,H_(k),其中k≥2,k色Ramsey数R(H_(1)..,H_(k))指满足以下性质的最小整数N:如果用k种颜色对完全图K的边任意进行染色,那么存在某个i(1≤i<k),使得K_(N)包含一个同构于H_(i)的i色子图.设C_(m)表示长度为m的圈,K_(1,n)表示阶数为n+1的星.本文系统介绍了星对四边形Ramsey数的最新研究进展,并概述了与四边形相关的Ramsey数,其中包括多色的情形.

关 键 词：multicolor Ramsey number polarity graph QUADRILATERAL STAR WHEEL BOOK 

分 类 号：O157.5[理学—数学]