A categorification for the signed chromatic polynomial
Combinatorics
2026-05-26 v1
Abstract
By coloring a signed graph by signed colors, one obtains the signed chromatic polynomial of the signed graph. For each signed graph we construct graded cohomology groups whose graded Euler characteristic yields the signed chromatic polynomial of the signed graph. We show that the cohomology groups satisfy a long exact sequence which corresponds to signed deletion-contraction rule. This work is motivated by Helme-Guizon and Rong's construction of the categorification for the chromatic polynomial of unsigned graphs.
Cite
@article{arxiv.2101.01661,
title = {A categorification for the signed chromatic polynomial},
author = {Zhiyun Cheng and Ziyi Lei and Yitian Wang and Yanguo Zhang},
journal= {arXiv preprint arXiv:2101.01661},
year = {2026}
}
Comments
19 pages, 5 figures