Chromatic symmetric functions and H-free graphs
Combinatorics
2017-09-12 v1
Abstract
Two celebrated conjectures in chromatic symmetric function theory concern the positivity chromatics symmetric functions of claw-free graphs. 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
Cite
@article{arxiv.1709.03354,
title = {Chromatic symmetric functions and H-free graphs},
author = {Angèle M. Hamel and Chính T. Hoàng and Jake E. Tuero},
journal= {arXiv preprint arXiv:1709.03354},
year = {2017}
}
Comments
12 pages