On the chromatic number of random d-regular graphs

• Published in: Advances in mathematics (New York. 1965) Vol. 223; no. 1; pp. 300 - 328
• Main Authors: Kemkes, Graeme, Pérez-Giménez, Xavier, Wormald, Nicholas
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.01.2010
• Subjects: Random graphs; Random graphs

In this work we show that, for any fixed d, random d-regular graphs asymptotically almost surely can be coloured with k colours, where k is the smallest integer satisfying d < 2 ( k − 1 ) log ( k − 1 ) . From previous lower bounds due to Molloy and Reed, this establishes the chromatic number to b...