Some Ramsey-Turán type problems and related questions
Some Ramsey-Turán type problems and related questions
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一些 Ramsey-Turán 类型的问题和相关问题
DOI：
10.1016/j.disc.2011.09.015
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
R. Schelp
中科院分区：
文献类型：
--
作者：
R. Schelp
在本文中，下面的Ramsey-Turán型问题是几个被讨论的问题之一。对于哪个图G，存在一个常数0<；c<；1使得当H是一个阶图时，δ(H)>；c|H|的Ramsey数r(G)，那么H的任何2边染色都包含G的一个单色副本？当G是有限最大度的奇圈、路或树时，考虑具有c的建议值的特定结果、猜想和问题。另一种变型是用一个阶数大致相同的平衡多部图来对图Kr(G)进行2边着色，得到相同的结果，即单色G。
In this paper the following Ramsey–Turán type problem is one of several addressed. For which graphs G does there exist a constant 0<c<1 such that when H is a graph of order the Ramsey number r(G) with δ(H)>c|H|, then any 2-edge coloring of H contains a monochromatic copy of G? Specific results, conjectures, and questions with suggested values for c are considered when G is an odd cycle, path, or tree of limited maximum degree. Another variant is to 2-edge color a replacement for the graph Kr(G)by a balanced multipartite graph of approximately the same order with the same consequence, a monochromatic G.