CHROMATIC POLYNOMIALS AND BIALGEBRAS OF GRAPHS

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International Electronic Journal of Algebra
Volume:30 Issue:30
CHROMATIC POLYNOMIALS AND BIALGEBRAS OF GRAPHS

CHROMATIC POLYNOMIALS AND BIALGEBRAS OF GRAPHS

Pages : 116-167

View : 46 | Download : 10

Publication Date : 2021-07-17

Article Type : Research Paper

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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