We show that i-triangulated graphs can be colored in linear time by applying lexicographic breadth-first search (abbreviated LexBFS) and the greedy coloring algorithm.

Given a graph G, a proper n − [p]-coloring is a mapping f : V (G) → 2{1,...,n} such that |f(v)| = p for any vertex v ∈ V (G) and f(v) ∩ f(u) = ∅ for any pair of adjacent vertices u and v. n − [p]-coloring is closely related to multicoloring. Finding multicoloring of induced subgraphs of the triangular lattice (called hexagonal graphs) has important applications in cellular networks. In this art...

In studying the scalability of optical networks, one problem arising involves coloring the vertices of the dimensional hypercube with as few colors as possible such that any two vertices whose Hamming distance is at most are colored differently. Determining the exact value of , the minimum number of colors needed, appears to be a difficult problem. In this paper, we improve the known lower and ...

An injective $k$-edge-coloring of a graph $G$ is an assignment colors, i.e. integers in $\{1, \ldots , k\}$, to the edges such that any two each incident with one distinct endpoint third edge, receive colors. The problem determining whether $k$-coloring exists called k-INJECTIVE EDGE-COLORING. We show 3-INJECTIVE EDGE-COLORING NP-complete, even for triangle-free cubic graphs, planar subcubic gr...

A dynamic k-coloring of a graph G is a proper k-coloring of the vertices of G such that every vertex of degree at least 2 in G will be adjacent to vertices with at least 2 different colors. The smallest number k for which a graph G can have a dynamic k-coloring is the dynamic chromatic number, denoted by χd(G). In this paper, we investigate the dynamic 3-colorings of claw-free graphs. First, we...

An injective coloring of a graph is a vertex labeling such that two vertices sharing a common neighbor get different labels. In this work we introduce and study what we call additive colorings. An injective coloring c : V (G) → Z of a graph G is an additive coloring if for every uv, vw in E(G), c(u)+ c(w) = 2c(v). The smallest integer k such that an injective (resp. additive) coloring of a give...

For fixed integers p and q, an edge coloring of Kn is called a (p, q)-coloring if the edges of Kn in every subset of p vertices are colored with at least q distinct colors. Let f(n, p, q) be the smallest number of colors needed for a (p, q)-coloring of Kn. In [3] Erdős and Gyárfás studied this function if p and q are fixed and n tends to infinity. They determined for every p the smallest q (= (...

A dynamic k-coloring of a graph G is a proper k-coloring of the vertices of G such that every vertex of degree at least 2 in G will be adjacent to vertices with at least 2 different colors. The smallest number k for which a graph G can have a dynamic k-coloring is the dynamic chromatic number, denoted by χd(G). In this paper, we investigate the dynamic 3-colorings of claw-free graphs. First, we...

In this paper we study the Optimal Cost Chromatic Partition (OCCP) problem for trees and interval graphs. The OCCP problem is the problem of coloring the nodes of a graph in such a way that adjacent nodes obtain diierent colors and that the total coloring costs are minimum. In this paper we rst give a linear time algorithm for the OCCP problem for trees. The OCCP problem for interval graphs is ...

A Gallai-coloring (G-coloring) is a generalization of 2-colorings of edges of complete graphs: a G-coloring of a complete graph is an edge coloring such that no triangle is colored with three distinct colors. Here we extend some results known earlier for 2-colorings to G-colorings. We prove that in every G-coloring of Kn there exists each of the following: 1. a monochromatic double star with at...