-λ coloring of graphs and Conjecture Δ ^ 2

λ-Coloring Matrogenic Graphs

This paper investigates a variant of the general problem of assigning channels to the stations of a wireless network when the graph representing the possible interferences is a matrogenic graph. In our problem, channels assigned to adjacent vertices must be at least two apart, while channels assigned to vertices at distance two must be different. An exact linear time algorithm is provided for t...

Approximations for λ-Coloring of Graphs

A λ-coloring of a graph G is an assignment of colors from the integer set {0, . . . , λ} to the vertices of the graph G such that vertices at distance at most two get different colors and adjacent vertices get colors which are at least two apart. The problem of finding λ-coloring with small or optimal λ arises in the context of radio frequency assignment. We show that the problem of finding the...

Acyclic edge coloring of planar graphs with Δ colors

An acyclic edge coloring of a graph is a proper edge coloring without bichromatic cycles. In 1978, it was conjectured that ∆(G) + 2 colors suffice for an acyclic edge coloring of every graph G [6]. The conjecture has been verified for several classes of graphs, however, the best known upper bound for as special class as planar graphs are, is ∆+12 [2]. In this paper, we study simple planar graph...

Strong edge-coloring of (3, Δ)-bipartite graphs

List-Coloring Claw-Free Graphs with Δ-1 Colors

We prove that if G is a quasi-line graph with ∆(G) > ω(G) and ∆(G) ≥ 69, then χOL(G) ≤ ∆(G) − 1. Together with our previous work, this implies that if G is a claw-free graph with ∆(G) > ω(G) and ∆(G) ≥ 69, then χl(G) ≤ ∆(G)− 1.

Edge-coloring Vertex-weightings of Graphs

Let $G=(V(G),E(G))$ be a simple, finite and undirected graph of order $n$. A $k$-vertex weightings of a graph $G$ is a mapping $w: V(G) to {1, ldots, k}$. A $k$-vertex weighting induces an edge labeling $f_w: E(G) to N$ such that $f_w(uv)=w(u)+w(v)$. Such a labeling is called an {it edge-coloring k-vertex weightings} if $f_{w}(e)not= f_{w}(echr(chr(chr('39')39chr('39'))39chr(chr('39')39chr('39'...