Breaking the rhythm on graphs

We study graph colorings avoiding periodic sequences with large number of blocks on paths. The main problem is to decide, for a given class of graphs F, if there are absolute constants t, k such that any graph from the class has a t-coloring with no k identical blocks in a row appearing on a path. The minimum t for which there is some k with this property is called the rhythm threshold of F, denoted by t(F). For instance, we show that the rhythm threshold of graphs of maximum

• Type: Journal
• Year: 2008
• Where: DM
• Authors: Noga Alon, Jaroslaw Grytczuk
• Keywords: DM 2008, Graph Colorings, Periodic Sequences, Rhythm Threshold