2-Distance Colorings of Integer Distance Graphs

Edge colorings and total colorings of integer distance graphs

Algorithms for Finding Distance-Edge-Colorings of Graphs

For a bounded integer , we wish to color all edges of a graph G so that any two edges within distance have different colors. Such a coloring is called a distance-edge-coloring or an -edge-coloring of G. The distance-edge-coloring problem is to compute the minimum number of colors required for a distance-edge-coloring of a given graph G. A partial k-tree is a graph with tree-width bounded by a f...

Recoloring graphs via tree decompositions

Let k be an integer. Two vertex k-colorings of a graph are adjacent if they differ on exactly one vertex. A graph is k-mixing if any proper k-coloring can be transformed into any other through a sequence of adjacent proper k-colorings. Jerrum proved that any graph is k-mixing if k is at least the maximum degree plus two. We first improve Jerrum’s bound using the grundy number, which is the wors...

Channel Assignment with Separation for Interference Avoidance in Wireless Networks

Given an integer > 1, a vector ð 1; 2; . . . ; ÿ1Þ of nonnegative integers, and an undirected graph G 1⁄4 ðV ;EÞ, an Lð 1; 2; . . . ; ÿ1Þ-coloring of G is a function f from the vertex set V to a set of nonnegative integers such that jfðuÞ ÿ fðvÞj i, if dðu; vÞ 1⁄4 i; 1 i ÿ 1, where dðu; vÞ is the distance (i.e., the minimum number of edges) between the vertices u and v. An optimal Lð 1; 2; . . ...

DISTANCE k COLORINGS OF HAMMING GRAPHS

A coloring of the vertices of a graph G is a distance k coloring of G if and only if any two vertices lying on a path of length less than or equal to k are given different colors. Hamming graphs are Cartesian (or box) products of complete graphs. In this paper, we will consider the interaction between coding theory and distance k colorings of Hamming graphs.