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DESCRIPTION: For a graph G=(V\,E)\, the chromatic polynomial X_G counts the
number of vertex colourings as a function of number of colours. Stanley’s
reciprocity theorem connects the chromatic polynomial with the enumeration
of acyclic orientations of G. One way to prove the reciprocity result is vi
a the decomposition of chromatic polynomials as the sum of order polynomial
s over all acyclic orientations. From the Discrete Geometry perspective\, t
he decomposition is as the sum of Ehrhart polynomials through real braid ar
rangement. Beck\, Bogart\, and Pham proved the analogue of this reciprocity
theorem for the strong chromatic polynomials for mixed graph. Dohmen–Pöni
tz–Tittmann provided a new two variable generalization of the chromatic pol
ynomial for undirected graphs. We extend this bivariate chromatic polynomia
l to mixed graphs\, provide a deletion-contraction like formula and study t
he colouring function geometrically via hyperplane arrangements.
DTSTAMP:20201215T153200
DTSTART:20210104T140000
CLASS:PUBLIC
LOCATION:online
SEQUENCE:0
SUMMARY:Sampada Kolhatkar: Bivariate chromatic polynomials of mixed graphs
UID:107739076@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20210104-L-Kolhatkar.html
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