@Article{Schiermeyer2017,
author = "Schiermeyer, Ingo",
title = "On the chromatic number of (P<sub>5</sub>,windmill)-free graphs",
journal = "Opuscula Math.",
year = "2017",
volume = "37",
number = "4",
pages = "609--615",
doi = "http://dx.doi.org/10.7494/OpMath.2017.37.4.609",
url = "http://dx.doi.org/10.7494/OpMath.2017.37.4.609",
abstract = "In this paper we study the chromatic number of \((P_5, windmill)\)-free graphs. For integers \(r,p\geq 2\) the windmill graph \(W_{r+1}^p=K_1 \vee pK_r\) is the graph obtained by joining a single vertex (the center) to the vertices of \(p\) disjoint copies of a complete graph \(K_r\). Our main result is that every \((P_5, windmill)\)-free graph \(G\) admits a polynomial \(\chi\)-binding function. Moreover, we will present polynomial \(\chi\)-binding functions for several other subclasses of \(P_5\)-free graphs.",
keywords = "vertex colouring, perfect graphs, \(\chi\)-binding function, forbidden induced subgraph",
issn = "1232-9274"
}