CHROMATIC POLYNOMIALS AND BIALGEBRAS OF GRAPHS

Year 2021, , 116 - 167, 17.07.2021

Loic Foıssy

https://doi.org/10.24330/ieja.969651

Cited By: 1

Abstract

The chromatic polynomial is characterized as the unique polynomial invariant of graphs, compatible with two interacting bialgebras structures:
the first coproduct is given by partitions of vertices into two parts, the second one by a contraction-extraction process.
This gives Hopf-algebraic proofs of Rota's result on the signs of coefficients of chromatic polynomials and of Stanley's interpretation
of the values at negative integers of chromatic polynomials. We also consider chromatic symmetric functions and their noncommutative versions.

Keywords

Bialgebras in cointeraction, chromatic polynomial, chromatic symmetric function

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