This is a book about graph homomorphisms. Graph theory is now an established discipline
but the study of graph homomorphisms has only recently begun to gain wide acceptance …

We show that planar graphs have bounded queue-number, thus proving a conjecture of
Heath et al.[66] from 1992. The key to the proof is a new structural tool called layered …

Graph coloring has been employed since the 1980s to efficiently compute sparse Jacobian
and Hessian matrices using either finite differences or automatic differentiation. Several …

A vertex coloring of a graph G is called acyclic if no two adjacent vertices have the same
color and there is no two-colored cycle in G. The acyclic chromatic number of G, denoted by …

We define the notions tree-depth and upper chromatic number of a graph and show their
relevance to local–global problems for graph partitions. In particular we show that the upper …

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 …

A vertex colouring of a graph $ G $ is" nonrepetitive" if $ G $ contains no path for which the
first half of the path is assigned the same sequence of colours as the second half. Thue's …

We introduce classes of graphs with bounded expansion as a generalization of both proper
minor closed classes and degree bounded classes. Such classes are based on a new …

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 …

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