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Why Almost Allk-Colorable Graphs Are Easy to Color

✍ Scribed by Amin Coja-Oghlan; Michael Krivelevich; Dan Vilenchik


Publisher
Springer
Year
2009
Tongue
English
Weight
910 KB
Volume
46
Category
Article
ISSN
1433-0490

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Almost all graphs with average degree 4
✍ Dimitris Achlioptas; Cristopher Moore πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 323 KB

We analyze a randomized version of the Brelaz heuristic on sparse random graphs. We prove that almost all graphs with average degree dp4:03; i.e., Gðn; p ¼ d=nÞ; are 3-colorable and that a constant fraction of all 4-regular graphs are 3-colorable.