## 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
Sparse Anti-Ramsey Graphs
β Scribed by Y. Kohayakawa; T. Luczak
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 269 KB
- Volume
- 63
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
β¦ Synopsis
It is shown that for every (l \geqslant 3) there exists a graph (G) of girth / such that in any proper edge-colouring of (G) one may find a cycle of length / all of whose edges are given different colours. 1995 Academic Press. Inc.
π SIMILAR VOLUMES
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
## 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
Let G = (V, E ) be a graph on n vertices with average degree t 2 1 in which for every vertex u E V the induced subgraph on the set of all neighbors of u is r-colorable. We show that the independence number of G is at least log t , for some absolute positive constant c. This strengthens a well-known
## Abstract For each fixed __k__ββ₯β0, we give an upper bound for the girth of a graph of order __n__ and size __n__β+β__k__. This bound is likely to be essentially best possible as __n__ββββ. Β© 2002 Wiley Periodicals, Inc. J Graph Theory 39: 194β200, 2002; DOI 10.1002/jgt.10023