We consider a class of graphs on n vertices, called (d,f)-arrangeable graphs. This class of graphs contains all graphs of bounded degree d, and all df-arrangeable graphs, a class introduced by Chen and Schelp in 1993. In 1992, a variation of the Regularity Lemma of Szemer6di was introduced by Eaton
On the Ramsey Number of Sparse 3-Graphs
✍ Scribed by Brendan Nagle; Sayaka Olsen; Vojtěch Rödl; Mathias Schacht
- Book ID
- 106047728
- Publisher
- Springer Japan
- Year
- 2008
- Tongue
- English
- Weight
- 246 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0911-0119
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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