On the Chromatic Number of (\(P_6\), Diamond)-Free Graphs

Original Paper
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Abstract

In this paper, we first show that every (\(P_6\), diamond, \(K_4\))-free graph is 6-colorable. We also give an example of a (\(P_6\), diamond, \(K_4\))-free graph G with \(\chi (G)\) \( = 6\). Further, we show that for every (\(P_6\), diamond)-free graph G, the chromatic number of G is upper bounded by a linear function of its clique number. This generalizes some known results in the literature.

Keywords

Graph classes \(P_6\)-free graphs Diamond-free graphs Chromatic number Clique number 

Notes

Acknowledgements

The first author thanks Mathew C.Francis for his comments. The authors are grateful to the anonymous referees for their helpful suggestions and remarks.

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Copyright information

© Springer Japan KK, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Computer Science UnitIndian Statistical Institute, Chennai CentreChennaiIndia
  2. 2.Department of MathematicsIndian Institute of Technology MadrasChennaiIndia

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