A parity walk in an edge-coloring of a graph is a walk along which each color is used an even number of times. Let p(G) be the least number of colors in an edge-coloring of G having no parity path (a parity edge-coloring). Let p̂(G) be the least number of colors in an edge-coloring of G having no open parity walk (a strong parity edge-coloring). Always p̂(G) ≥ p(G) ≥ χ′(G). We prove that p̂(Kn) = ...

Acyclic-coloring of a graph G = (V; E) is a partitioning of V , such that the induced subgraph of each partition is acyclic. The minimum number of such partitions of V is deened as the vertex arboricity of G. An O(n) algorithm (n = jV j) for acyclic-coloring of planar graphs with 3 colors is presented. Next, an O(n 2) heuristic is proposed which produces a valid acyclic-2-coloring of a planar g...

The pre-coloring extension problem consists, given a graph G and a subset of nodes to which some colors are already assigned, in finding a coloring of G with the minimum number of colors which respects the pre-coloring assignment. This can be reduced to the usual coloring problem on a certain contracted graph. We prove that pre-coloring extension is polynomial for complements of Meyniel graphs....

Acyclic-coloring of a graph G = (V;E) is a partitioning of V , such that the induced subgraph of each partition is acyclic. The minimumnumber of such partitions of V is de ned as the vertex arboricity of G. An O(n) algorithm (n = jV j) for acyclic-coloring of planar graphs with 3 colors is presented. Next, an O(n) heuristic is proposed which produces a valid acyclic-2-coloring of a planar graph...

The pre-coloring extension problem consists, given a graph G and a subset of nodes to which some colors are already assigned, in nding a coloring of G with the minimum number of colors which respects the pre-coloring assignment. This can be reduced to the usual coloring problem on a certain contracted graph. We prove that pre-coloring extension is polynomial for complements of Meyniel graphs. W...

background : skin cancer is the most common malignancy in the world. thus, the aim of this study was to determine the incidence trend of skin cancer in isfahan province, iran. methods: the present cross-sectional study was conducted using data registered during 2004-2008 in the disease management center and cancer registry system of the ministry of health and medical education. the trend of ski...

In this paper we propose a deterministic parallel graph coloring algorithm that enables Multi-Coloring in parallel for sparse undirected graphs by coarse-grained segmentation and symmetry breaking. The proposed algorithm is implemented and tested on standard problem instances from engineering applications and benchmarked against various deterministic graph coloring algorithms. Quantified result...

We study interval coloring problems and present new upper and lower bounds for several variants. We are interested in four problems, online coloring of intervals with and without bandwidth and a new problem called lazy online coloring again with and without bandwidth. We consider both general interval graphs and unit interval graphs. Specifically, we establish the difference between the two mai...

We define a variant of the H-coloring problem where the number of preimages of certain vertices is predetermined as part of the problem input. We consider the decision and the counting version of the problem, namely the restrictive H-coloring and the restrictive #H-coloring problems, and we provide a dichotomy theorem determining the H’s for which the restrictive H-coloring problem is either NP...

Let G(V,E) be a k-uniform hypergraph. A hyperedge e ∈ E is said to be properly (r, p) colored by an r-coloring of vertices in V if e contains vertices of at least p distinct colors in the rcoloring. An r-coloring of vertices in V is called a strong (r, p) coloring if every hyperedge e∈E is properly (r, p) colored by the r-coloring. We study the maximum number of hyperedges that can be properly ...