## Abstract It is shown that the Ramsey number of any graph with __n__ vertices in which no two vertices of degree at least 3 are adjacent is at most 12__n__. In particular, the above estimate holds for the Ramsey number of any __n__βvertex subdivision of an arbitrary graph, provided each edge of t
Anti-Ramsey Numbers of Subdivided Graphs
β Scribed by Tao Jiang
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 88 KB
- Volume
- 85
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
β¦ Synopsis
Given a positive integer n and a family F of graphs, the anti-Ramsey number f(n, F) is the maximum number of colors in an edge-coloring of K n such that no subgraph of K n belonging to F has distinct colors on its edges. The Tura Β΄n number ex(n, F) is the maximum number of edges of an n-vertex graph that does not contain a member of F as a subgraph.
π SIMILAR VOLUMES
## Abstract Given a graph __H__ and a positive integer __n__, __AntiβRamsey number AR__(__n, H__) is the maximum number of colors in an edgeβcoloring of __K__~__n__~ that contains no polychromatic copy of __H__. The antiβRamsey numbers were introduced in the 1970s by ErdΕs, Simonovits, and SΓ³s, who
## Abstract Given two graphs __G__ and __H__, let __f__(__G__,__H__) denote the minimum integer __n__ such that in every coloring of the edges of __K__~__n__~, there is either a copy of __G__ with all edges having the same color or a copy of __H__ with all edges having different colors. We show tha
## Abstract The Ramsey number __R__(__G__~1~,__G__~2~) of two graphs __G__~1~ and __G__~2~ is the least integer __p__ so that either a graph __G__ of order __p__ contains a copy of __G__~1~ or its complement __G__^c^ contains a copy of __G__~2~. In 1973, Burr and ErdΕs offered a total of $25 for se