Locally Ramsey properties of graphs
β Scribed by S. G. Sal'nikov
- Publisher
- SP MAIK Nauka/Interperiodica
- Year
- 1988
- Tongue
- English
- Weight
- 382 KB
- Volume
- 43
- Category
- Article
- ISSN
- 0001-4346
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
For a graph F and natural numbers a 1 ; . . . ; a r ; let F ! Γ°a 1 ; . . . ; a r Γ denote the property that for each coloring of the edges of F with r colors, there exists i such that some copy of the complete graph K ai is colored with the ith color. Furthermore, we write Γ°a 1 ; . . . ; a r Γ ! Γ°b
For graphs F, G 1 , ..., G r , we write F Q (G 1 , ..., G r ) if for every coloring of the vertices of F with r colors there exists i, i=1, 2, ..., r, such that a copy of G i is colored with the ith color. For two families of graphs G 1 , ..., G r and H 1 , ..., H s , by .., H s ) for every graph F
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 We consider the problem of which graph invariants have a certain property relating to Ramsey's theorem. Invariants which have this property are called Ramsey functions. We examine properties of chains of graphs associated with Ramsey functions. Methods are developed which enable one to
This paper establishes that the local k-Ramsey number R(K m , k -loc) is identical with the mean k-Ramsey number R(K m , k -mean). This answers part of a question raised by Caro and Tuza.