" This is the first book to comprehensively cover chromatic polynomials of graphs. It includes
most of the known results and unsolved problems in the area of chromatic polynomials …

Given a list assignment for a graph, list packing asks for the existence of multiple pairwise
disjoint list colorings of the graph. Several papers have recently appeared that study the …

We review the work of Dominic Welsh (1938-2023), tracing his remarkable influence through
his theorems, expository writing, students, and interactions. He was particularly adept at …

Let μ (G) μ (G) denote the mean color number of a graph G. Dong proposed two mean color
conjectures. One is that for any graph G and a vertex w in G with d (w) ≥ 1 d (w)≥ 1, if H is a …

In 2015, Brown and Erey conjectured that every $2 $-connected graph $ G $ on $ n $
vertices with chromatic number $ k\geq 4$ has at most $(x-1) _ {k-1}\big ((x-1)^{n-k+ 1}+ …

The mean color number of an $ n $-vertex graph $ G $, denoted by $\mu (G) $, is the
average number of colors used in all proper $ n $-colorings of $ G $. For any graph $ G …

Graph coloring is the mathematical model for studying problems related to conflict-free
allocation of resources. DP-coloring (also known as correspondence coloring) of graphs is a …

Let μ (G) denote the mean colour number of a graph G. Mosca discovered some
counterexamples which disproved a conjecture proposed by Bartels and Welsh that if H is a …

The birthday paradox states that there is at least a 50% chance that some two out of twenty-
three randomly chosen people will share the same birth date. The calculation for this …

In this note we consider s s-chromatic polynomials for finite simplicial complexes. When s= 1
s= 1, the 1 1-chromatic polynomial is just the usual graph chromatic polynomial of the 1 1 …