Probabilistic methods in coloring and decomposition problems

Probabilistic methods in coloring and decomposition problems

Numerous problems in Graph Theory and Combinatorics can be formulated in terms of the existence of certain colorings of graphs or hypergraphs. Many of these problems can be solved or partially solved by applying probabilistic arguments. In this paper we discuss several examples that illustrate the methods used. This is mainly a survey paper, but it contains some new results as well.

Probabilistic Methods on Erdos Problems

There are four parts: an introduction, a set of solutions to the Ramsey problem, some enumeration problems, and the Gyarfas-Lehel conjecture. Section

Probabilistic Methods for Coordination Problems

Probabilistic Methods for Decomposition Dimension of Graphs

In a graph G, the distance from an edge e to a set F ⊆ E(G) is the vertex distance from e to F in the line graph L(G). For a decomposition of E(G) into k sets, the distance vector of e is the k-tuple of distances from e to these sets. The decomposition dimension dec(G) of G is the smallest k such that G has a decomposition into k sets so that the distance vectors of the edges are distinct. For ...

Decomposition Methods and Network Design Problems