![]() 339(8), 2100–2112 (2016)īirkhoff, G.D.: A determinant formula for the number of ways of coloring a map. Graph Theory 88, 521–546 (2018)īernshteyn, A., Kostochka, A.: On differences between DP-coloring and list coloring. ![]() Algorithms 54(4), 653–664 (2019)īernshteyn, A., Kostochka, A.: Sharp Dirac’s theorem for DP-critical graphs. 345, 113093 (2022)īernshteyn, A.: The asymptotic behavior of the correspondence chromatic number. The tools we develop along with the Rearrangement Inequality give a new method for determining the DP color function of all Theta graphs and the dual DP color function of all Generalized Theta graphs.īecker, J., Hewitt, J., Kaul, H., Maxfield, M., Mudrock, J., Spivey, D., Thomason, S., Wagstrom, T.: The DP color function of joins and vertex-gluings of graphs. We show that the DP color function is not chromatic-adherent by studying the DP color function of Generalized Theta graphs. It is not known if the list color function and the DP color function are chromatic-adherent. A function f is chromatic-adherent if for every graph G, \(f(G,a) = P(G,a)\) for some \(a \ge \chi (G)\) implies that \(f(G,m) = P(G,m)\) for all \(m \ge a\). Counting function analogues of the chromatic polynomial have been introduced and studied for list colorings: \(P_^*(G,m)\). The chromatic polynomial of a graph is an extensively studied notion in combinatorics since its introduction by Birkhoff in 1912 denoted P( G, m), it equals the number of proper m-colorings of graph G. ![]() ![]() DP-coloring (also called correspondence coloring) is a generalization of list coloring that has been widely studied in recent years after its introduction by Dvořák and Postle in 2015. ![]()
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