… As our goal is to study random d-regular graphs on n vertices, we will always assume
that dn is even. To get a handle on the … The graph coloring problem is just a particular …

… Let G, denote a random graph sampled uniformly from REG(n, r). We use tl and x for
independence and chromatic numbers, respectively. In random graph theory, these have been …

… We prove that with high probability the chromatic number of a random d-regular graph is k,
k + 1, or k + 2. … If this is true, our results imply that for d in “good” intervals (uk,ck) whp the …

… fixed d, random d-regular graphs asymptotically almost surely … , this establishes the chromatic
number to be asymptotically … and thus the chromatic number is exactly determined. Hence …

… Let Gr denote a graph chosen uniformly at random from the set Gr of simple r-regular graphs
with vertex set V = {1, 2,...,n}. We consider the independence and chromatic number of Gr …

… The chromatic number of random regular graphs has attracted … For the uniform model Gn,d
of d-regular graphs on n labelled … the chromatic number of the random 5-regular graph aas …

… is highly concentrated when the graphs are sparse enough. … concentration result in the random
regular graph model G n , … typical” random regular graphs, and specifically, the number of …

… random graph Gn,p is its chromatic number, which we denote by χ(Gn,p). Trivially for every
graph χ(… This provides a lower bound on the chromatic number of the random graph, showing …

… complete answer by determining the chromatic number of |$G… Its use in the context of phase
transitions in random discrete … on which the chromatic number of the random |$d$|-regular is …

… Thus Theorem 1.2 shows that the game chromatic number of Gn,p is at most (… its chromatic
number. Having proved Theorem 1.2, we extend the results to the random d-regular graph …