After a brief historical account, a few simple structural theorems about plane graphs useful
for coloring are stated, and two simple applications of discharging are given. Afterwards, the …

Coloring with no 2-colored P4’s Page 1 Coloring with no 2-colored P4’s Michael O. Albertson
Department of Mathematics Smith College Northhampton, MA 01063 albertson@smith.edu …

A star coloring of an undirected graph G is a proper vertex coloring of G (ie, no two
neighbors are assigned the same color) such that any path of length 3 in G is not bicolored …

Vertex and edge colorability are two graph problems that are NP-hard in general. We show
that both problems remain difficult even for graphs without short cycles, ie, without cycles of …

In this paper, we give a relatively simple though very efficient way to color the d-dimensional
grid G (n1, n2,…, nd)(with ni vertices in each dimension 1⩽ i⩽ d), for two different types of …

It is known that the acyclic chromatic number of a subcubic graph is at most four, and its
acyclic edge chromatic number is at most five. We present algorithms that prove these two …

Acyclic colouring of 1-planar graphs - ScienceDirect Skip to main contentSkip to article Elsevier
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A\emph (k, t)-track layout of a graph G consists of a (proper) vertex t-colouring of G, a total
order of each vertex colour class, and a (non-proper) edge k-colouring such that between …

Acyclic, Star and Oriented Colourings of Graph Subdivisions Page 1 Discrete Mathematics
and Theoretical Computer Science 7, 2005, 37–50 Acyclic, Star and Oriented Colourings of …

In this paper, we deal with the notion of star coloring of graphs. A star coloring of an
undirected graph G is a proper vertex coloring of G (ie, no two neighbors are assigned the …