The Hopf monoid and the basic invariant of directed graphs
Combinatorics
2019-07-29 v1 Geometric Topology
Abstract
Aguiar and Ardila defined the Hopf monoid GP of generalized permutahedra and showed that it contains many submonoids that correspond to combinatorial objects. They also give a basic polynomial invariant of generalized permutahedra, which then specializes to the submonoids. We define the Hopf monoid of directed graphs and show that it also embeds in GP. The resulting basic invariant coincides with the strict chromatic polynomial of Awan and Bernardi.
Keywords
Cite
@article{arxiv.1907.10825,
title = {The Hopf monoid and the basic invariant of directed graphs},
author = {Keiju Kato},
journal= {arXiv preprint arXiv:1907.10825},
year = {2019}
}
Comments
18pages, 3 figures. arXiv admin note: text overlap with arXiv:1709.07504 by other authors