Two cycle-chord graphs are $e$-positive
Combinatorics
2021-12-14 v1
Abstract
We prove Gebhard and Sagan's -positivity of the line graphs of tadpoles in noncommuting variables. This implies the -positivity of these line graphs. We then extend this -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