English

Two cycle-chord graphs are $e$-positive

Combinatorics 2021-12-14 v1

Abstract

We prove Gebhard and Sagan's (e)(e)-positivity of the line graphs of tadpoles in noncommuting variables. This implies the ee-positivity of these line graphs. We then extend this (e)(e)-positivity result to that of certain cycle-chord graphs, and derive the bivariate generating function of all cycle-chord graphs.

Cite

@article{arxiv.2112.06679,
  title  = {Two cycle-chord graphs are $e$-positive},
  author = {David G. L. Wang and Monica M. Y. Wang},
  journal= {arXiv preprint arXiv:2112.06679},
  year   = {2021}
}

Comments

15 pages, 4 figures

R2 v1 2026-06-24T08:15:02.430Z