Opuscula Math. 37, no. 4 (2017), 609-615

Opuscula Mathematica

On the chromatic number of (P5,windmill)-free graphs

Ingo Schiermeyer

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.

Mathematics Subject Classification: 05C15, 05C17.

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  • Ingo Schiermeyer
  • Technische Universität Bergakademie Freiberg, Institut für Diskrete Mathematik und Algebra, 09596 Freiberg, Germany
  • Communicated by Hao Li.
  • Received: 2016-07-25.
  • Accepted: 2016-11-09.
  • Published online: 2017-04-28.
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Cite this article as:
Ingo Schiermeyer, On the chromatic number of (P5,windmill)-free graphs, Opuscula Math. 37, no. 4 (2017), 609-615, http://dx.doi.org/10.7494/OpMath.2017.37.4.609

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