Polynomial iterative algorithms for coloring and analyzing random graphs.

[Article] Polynomial iterative algorithms for coloring and analyzing random graphs

Minimum Coloring Random and Semi-Random Graphs in Polynomial Expected Time

We present new algorithms for k-coloring and minimum (x(G)-) coloring random and semi-random kcolorable graphs in polynomial expected time. The random graphs are drawn from the G(n,p, k) model and the semi-random graphs are drawn from the G s ~ ( n , p , k) model. In both models, an adversary initially splits the n vertices into IC color classes, each of size @(n). Then the edges between vertic...

Randomly coloring sparse random graphs with fewer colors than the maximum degree

We analyze Markov chains for generating a random k-coloring of a random graph Gn,d/n. When the average degree d is constant, a random graph has maximum degree log n/ log log n, with high probability. We efficiently generate a random k-coloring when k = Ω(log log n/ log log log n), i.e., with many fewer colors than the maximum degree. Previous results hold for a more general class of graphs, but...

On the Minimum Load Coloring Problem

Given a graph G = (V,E) with n vertices, m edges and maximum vertex degree ∆, the load distribution of a coloring φ : V → {red, blue} is a pair dφ = (rφ, bφ), where rφ is the number of edges with at least one end-vertex colored red and bφ is the number of edges with at least one end-vertex colored blue. Our aim is to find a coloring φ such that the (maximum) load, lφ := 1 m · max{rφ, bφ}, is mi...

Tenacity and some other Parameters of Interval Graphs can be computed in polynomial time

In general, computation of graph vulnerability parameters is NP-complete. In past, some algorithms were introduced to prove that computation of toughness, scattering number, integrity and weighted integrity parameters of interval graphs are polynomial. In this paper, two different vulnerability parameters of graphs, tenacity and rupture degree are defined. In general, computing the tenacity o...