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Interpreting the (signed) chromatic polynomial coefficients via hyperplane arrangements
Published Web Location
https://doi.org/10.5070/C6.69943Abstract
A recent result of Lofano and Paolini expresses the characteristic polynomial of a real hyperplane arrangement in terms of a projection statistic on the regions of the arrangement. We use this result to give an alternative proof for Greene and Zaslavsky's interpretation for the coefficients of the chromatic polynomial of a graph and further generalize this interpretation to signed graphs. We also show that this projection statistic has a nice combinatorial interpretation in the case of the braid arrangement, which generalizes to graphical arrangements of natural unit interval graphs.
Mathematics Subject Classifications: 52C35, 05A15, 05C15, 05C22
Keywords: Hyperplane arrangements, chromatic polynomials, signed graphs