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has been cited by the following article:

• TITLE: On the Chromatic Number of (P5, C5, Cricket)-Free Graphs

  AUTHORS: Weilun Xu

  KEYWORDS: P5-Free Graphs, Chromatic Number, X-Boundedness

  JOURNAL NAME: Engineering, Vol.14 No.3, March 25, 2022

  ABSTRACT: For a graph G, let be the chromatic number of G. It is well-known that holds for any graph G with clique number . For a hereditary graph class , whether there exists a function f such that holds for every has been widely studied. Moreover, the form of minimum such an f is also concerned. A result of Schiermeyer shows that every -free graph G with clique number has . Chudnovsky and Sivaraman proved that every -free with clique number graph is -colorable. In this paper, for any -free graph G with clique number , we prove that . The main methods in the proof are set partition and induction.