List Coloring of Random and Pseudo-Random Graphs

List Coloring of Random and Pseudo-Random Graphs

The choice number of a graph G is the minimum integer k such that for every assignment of a set S(v) of k colors to every vertex v of G, there is a proper coloring of G that assigns to each vertex v a color from S(v). It is shown that the choice number of the random graph G(n, p(n)) is almost surely Θ( np(n) ln(np(n)) ) whenever 2 < np(n) ≤ n/2. A related result for pseudo-random graphs is prov...

List oloring of random and pseudo-random graphs

List total coloring of pseudo-outerplanar graphs

A graph is pseudo-outerplanar if each of its blocks has an embedding in the plane so that the vertices lie on a fixed circle and the edges lie inside the disk of this circle with each of them crossing at most one another. It is proved that every pseudo-outerplanar graph with maximum degree ∆ ≥ 5 is totally (∆ + 1)-choosable.

Coloring Random Graphs

We present a randomized polynomial time algorithm that colors almost every graph on n vertices in n/(log2 n+ c √ log2 n) colors for every positive constant c.  1998 Published by Elsevier Science B.V. All rights reserved.

Coloring random graphs

We study the graph coloring problem over random graphs of finite average connectivity c. Given a number q of available colors, we find that graphs with low connectivity admit almost always a proper coloring, whereas graphs with high connectivity are uncolorable. Depending on q, we find the precise value of the critical average connectivity c(q). Moreover, we show that below c(q) there exists a ...