@article{3682ec69cdaa443b85386a904ccdc915,
title = "Breaking the rhythm on graphs",
abstract = "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 degree at most d is between (d + 1) / 2 and d + 1. We give several general conditions for finiteness of t (F), as well as some connections to existing chromatic parameters. The question whether the rhythm threshold is finite for planar graphs remains open.",
keywords = "Graph coloring, Random graph, Rhythm threshold, Thue sequence",
author = "Noga Alon and Jaros{\l}aw Grytczuk",
note = "Funding Information: The first author was supported by an ISF grant and by a USA-Israeli BSF grant. The second author was supported by Grant KBN 1P03A 017 27. ",
year = "2008",
month = apr,
day = "28",
doi = "10.1016/j.disc.2007.07.063",
language = "אנגלית",
volume = "308",
pages = "1375--1380",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier B.V.",
number = "8",
}