The oriented chromatic polynomial of a oriented graph outputs the number of oriented $k$-colourings for any input $k$. We fully classify those oriented graphs for which the oriented graph has the same chromatic polynomial as the underlying simple graph, closing an open problem posed by Sopena. We find that such oriented graphs can be both identified and constructed in polynomial time as they are exactly the family of quasi-transitive oriented co-interval graphs. We study the analytic properties of this polynomial and show that there exist oriented graphs which have chromatic polynomials have roots, including negative real roots, that cannot be realized as the root of any chromatic polynomial of a simple graph.
@article{10_37236_8240,
author = {Danielle Cox and Christopher Duffy},
title = {Chromatic polynomials of oriented graphs},
journal = {The electronic journal of combinatorics},
year = {2019},
volume = {26},
number = {3},
doi = {10.37236/8240},
zbl = {1420.05082},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8240/}
}
TY - JOUR
AU - Danielle Cox
AU - Christopher Duffy
TI - Chromatic polynomials of oriented graphs
JO - The electronic journal of combinatorics
PY - 2019
VL - 26
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/8240/
DO - 10.37236/8240
ID - 10_37236_8240
ER -
%0 Journal Article
%A Danielle Cox
%A Christopher Duffy
%T Chromatic polynomials of oriented graphs
%J The electronic journal of combinatorics
%D 2019
%V 26
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/8240/
%R 10.37236/8240
%F 10_37236_8240
Danielle Cox; Christopher Duffy. Chromatic polynomials of oriented graphs. The electronic journal of combinatorics, Tome 26 (2019) no. 3. doi: 10.37236/8240
