Given a graph G, an automorphic edge(vertex)-coloring of G is a proper edge(vertex)-coloring such that each automorphism of the graph preserves the coloring. The automorphic chromatic index (number) is the least integer k for which G admits an automorphic edge(vertex)coloring with k colors. We show that it is NP-complete to determine the automorphic chromatic index and the automorphic chromatic...

Graph coloring and its generalizations are useful tools in modeling a wide variety of scheduling and assignment problems. In this paper we review several variants of graph coloring, such as precoloring extension, list coloring, multicoloring, minimum sum coloring, and discuss their applications in scheduling.

This article focuses on register assignment problems for heterogeneous register-set VLIW-DSP architectures. It is assumed that an instruction schedule has already been generated. The register assignment problem is equivalent to the well-known coloring of an interference graph. Typically, machine-related constraints are mapped onto the structure of the interference graph. Thereby favorable chara...

An adjacent vertex distinguishing edge-coloring or an avd-coloring of a simple graph G is a proper edge-coloring of G such that no pair of adjacent vertices meets the same set of colors. We prove that every graph with maximum degree ∆ and with no isolated edges has an avd-coloring with at most ∆ + 300 colors, provided that ∆ > 1020. AMS Subject Classification: 05C15

In this paper, we show that for every graph of maximum average degree bounded away from d, any (d + 1)-coloring can be transformed into any other one within a polynomial number of vertex recolorings so that, at each step, the current coloring is proper. In particular, it implies that we can transform any 8-coloring of a planar graph into any other 8-coloring with a polynomial number of recolori...

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...

A twin edge k-coloring of a graph G is a proper edge coloring of G with the elements of Zk so that the induced vertex coloring in which the color of a vertex v in G is the sum (in Zk) of the colors of the edges incident with v is a proper vertex coloring. The minimum k for which G has a twin edge k-coloring is called the twin chromatic index of G. Among the results presented are formulas for th...

Designing effective exact algorithms for graph coloring problem is still an interesting topic. Instead of getting only one best solution, two exact graph coloring algorithms, PexaCol (Partial best solutions Exact graph Coloring algorithm) and AexaCol (All best solutions Exact graph Coloring algorithm), have been proposed, which are able to obtain a best solution subset and all best solutions re...

We present a branching scheme for some Vertex Coloring Problems based on a new graph operator called extension. The extension operator is used to generalize the branching scheme proposed by Zykov for the basic problem to a broad class of coloring problems, such as the graph multicoloring, where each vertex requires a multiplicity of colors, the graph bandwidth coloring, where the colors assigne...

In this technical report we study different parallel graph coloring algorithms and their application to the incomplete-LU factorization. We implement graph coloring based on different heuristics and showcase their performance on the GPU. We also present a comprehensive comparison of level-scheduling and graph coloring approaches for the incomplete-LU factorization and triangular solve. We discu...