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Chromatic symmetric functions and H-free graphs

  • Angèle M. HamelEmail author
  • Chính T. Hoàng
  • Jake E. Tuero
Original Paper
  • 12 Downloads

Abstract

Using a graph and its colorings we can define a chromatic symmetric function. Stanley’s celebrated conjecture about the e-positivity of claw-free incomparability graphs has seen several related results, including one showing (\(claw, P_4\))-free graphs are e-positive. Here we extend the claw-free idea to general graphs and consider the e-positivity question for H-free graphs where \(H = \{claw, F\}\) and \(H=\){claw, F, co-F}, where F is a four-vertex graph. We settle the question for all cases except \(H=\){claw, co-diamond}, and we provide some partial results in that case.

Keywords

Chromatic symmetric function Claw-free graphs e-positive 

Notes

Acknowledgements

This work was supported by the Canadian Tri-Council Research Support Fund. The 1st and 2nd authors (A.M. Hamel and C.T. Hoàng) were each supported by individual NSERC Discovery Grants. The 3rd author (J.E. Tuero) was supported by an NSERC Undergraduate Student Research Award (USRA).

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Copyright information

© Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Physics and Computer ScienceWilfrid Laurier UniversityWaterlooCanada

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