Ramsey and Gallai-Ramsey numbers for stars with extra independent edges

被引:2
|
作者
Mao, Yaping [1 ,2 ]
Wang, Zhao [3 ]
Magnant, Colton [2 ,4 ]
Schiermeyer, Ingo [5 ]
机构
[1] Qinghai Normal Univ, Sch Math & Stat, Xining 810008, Qinghai, Peoples R China
[2] Acad Plateau Sci & Sustainabil, Xining 810008, Qinghai, Peoples R China
[3] China Jiliang Univ, Coll Sci, Hangzhou 310018, Peoples R China
[4] Clayton State Univ, Dept Math, Morrow, GA 30260 USA
[5] Tech Univ Bergakad Freiberg, Inst Diskrete Math & Algebra, D-09596 Freiberg, Germany
基金
美国国家科学基金会;
关键词
All Open Access; Green;
D O I
10.1016/j.dam.2020.05.003
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Given a graph G and a positive integer k, define the Gallai-Ramsey number to be the minimum number of vertices n such that any k-edge coloring of K-n contains either a rainbow (all different colored) triangle or a monochromatic copy of G. In this paper, we obtain general upper and lower bounds on the Gallai-Ramsey numbers for the graph G = S-t(r) obtained from a star of order t by including r extra independent edges between leaves of the star so there are r triangles and t - 2r - 1 pendant edges in S-t(r). We also prove some sharp results when r = 2. (C) 2020 Elsevier B.V. All rights reserved.
引用
收藏
页码:153 / 172
页数:20
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