𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On bounds for size Ramsey numbers of a complete tripartite graph

✍ Scribed by Izolda Gorgol

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
146 KB
Volume
164
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis

It will be shown that the (diagonal) size Ramsey number of K ..... is bounded below by c. 64n , 2 3oj2 ~n 2 and above by 2 Let F and G be graphs. The symbol F >---,G denotes that in any two-colouring (say red and blue) of edges of F a monochromatic copy of G is contained. The Ramsey number r(G) is the smallest integer r such that Kr >--~G. The size Ramsey number c < min[ \2--0-p--_2~ e--~l j ' \2(3p--~)7~el/(--P -~-1) ePJ f and of course such a constant exists. []

As for the upper bound we have only a very rough one.

πŸ“œ SIMILAR VOLUMES

The size Ramsey number of a complete bip
The size Ramsey number of a complete bipartite graph
✍ P. Erdo˝s; C.C. Rousseau πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 240 KB

Erd6s. P. and C.C. Rousseau, The size Ramsey number of a complete bipartite graph, Discrete Mathematics 113 (1993) 259-262. In this note we prove that the (diagonal) size Ramsey number of K,,.,, is bounded below by $2'2".

On the number of triangular embeddings o
On the number of triangular embeddings of complete graphs and complete tripartite graphs
✍ M. J. Grannell; M. Knor πŸ“‚ Article πŸ“… 2011 πŸ› John Wiley and Sons 🌐 English βš– 159 KB

## Abstract We prove that for every prime number __p__ and odd __m__>1, as __s__β†’βˆž, there are at least __w__ face 2‐colorable triangular embeddings of __K__~__w, w, w__~, where __w__ = __m__Β·__p__^__s__^. For both orientable and nonorientable embeddings, this result implies that for infinitely many

The ramsey numbers for stripes and one c
The ramsey numbers for stripes and one complete graph
✍ Peter Lorimer πŸ“‚ Article πŸ“… 1984 πŸ› John Wiley and Sons 🌐 English βš– 244 KB πŸ‘ 1 views

The Ramsey numbers M,,, n,P,, ..., n,P,), p > 2, are calculated. ## 1. Introduction One class of generalized Ramsey numbers that are known exactly are those for the graphs nP2 which consist of n disjoint paths of length 2; E. J. Cockayne and the author proved in 111 that d r(nlp2, ..., n d P 2 ) =