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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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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

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## 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 Erdős offered a total of $25 for se

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✍ Noga Alon 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 409 KB 👁 1 views

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