‎For a coloring $c$ of a graph $G$‎, ‎the edge-difference coloring sum and edge-sum coloring sum with respect to the coloring $c$ are respectively‎ ‎$sum_c D(G)=sum |c(a)-c(b)|$ and $sum_s S(G)=sum (c(a)+c(b))$‎, ‎where the summations are taken over all edges $abin E(G)$‎. ‎The edge-difference chromatic sum‎, ‎denoted by $sum D(G)$‎, ‎and the edge-sum chromatic sum‎, ‎denoted by $sum S(G)$‎, ‎a...

Coja-Oghlan and Taraz (2004) presented a graph coloring algorithm that has expected linear running time for random graphs with edge probability p satisfying np ≤ 1.01. In this work, we develop their analysis by exploiting generating function techniques. We show that, in fact, their algorithm colors Gn,p with the minimal number of colors and has expected linear running time, provided that np ≤ 1...

In the present dissertation we investigate structural and algorithmic aspects of the frequency assignment problem in mobile telephone networks. This problem is of particular interest for the graph theory because of its close relationship to graph coloring. The frequency assignment problem includes the characteristic features of T-coloring, list coloring, and set coloring, and belongs thereby to...

Abstract A linear equation with coefficients in $\mathbb{F}_q$ is common if the number of monochromatic solutions any two-coloring $\mathbb{F}_q^{\,n}$ asymptotically (as $n \to \infty$) at least expected a random two-coloring. The Sidorenko dense subset set same density. In this paper, we characterize those equations which are common, and Sidorenko. main novelty construction based on choosing ...

This thesis studies both several extremal problems about coloring of graphs and a labeling problem on graphs. We consider colorings of graphs that are either embeddable in the plane or have low maximum degree. We consider three problems: coloring the vertices of a graph so that no adjacent vertices receive the same color, coloring the edges of a graph so that no adjacent edges receive the same ...

so that every square is covered by exactly one domino? In other words, can R be tiled by vertical and horizontal dominoes? The coloring gives the answer to this well-known problem away. The region R has 32 black squares and 30 white squares. Since each domino covers exactly one black and one white square, no tiling is possible. The aim of this article is to explain a way to tackle tiling proble...

Finding a good graph coloring quickly is often a crucial phase in the development of eecient, parallel algorithms for many scientiic and engineering applications. In this paper we consider the problem of solving the graph coloring problem itself in parallel. We present a simple and fast parallel graph coloring heuristic that is well suited for shared memory programming and yields an almost line...

We give a simpler proof of Seymour’s Theorem on edge-coloring series-parallel multigraphs and derive a linear-time algorithm to check whether a given series-parallel multigraph can be colored with a given number of colors.

Dynamic detection and elimination of symmetry in constraints, is in general a hard task, but in Not-Equals binary constraint networks, the symmetry conditions can be simplified. In this paper, we extend the principle of symmetry to dominance in Not-Equals Constraint Networks and show how dominated values are detected and eliminated at each node of the search tree. A Linear time complexity algor...

We consider the problem of coloring a grid using k colors with the restriction that in each row and each column has an specific number of cells of each color. In an already classical result, Ryser obtained a necessary and sufficient condition for the existence of such a coloring when two colors are considered. This characterization yields a linear time algorithm for constructing such a coloring...