This is a survey of distance-regular graphs. We present an introduction to distance-regular
graphs for the reader who is unfamiliar with the subject, and then give an overview of some …

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 …

We examine the effect of bounding the diameter for a number of natural and well-studied
variants of the COLOURING problem. A colouring is acyclic, star, or injective if any two …

If G is a simple graph, then con (G), the common neighborhood graph of G, has the same
vertex set as G, and two vertices of con (G) are adjacent if they have a common neighbor in …

An injective k-edge-coloring of a graph G is an assignment of colors, ie integers in {1,…, k},
to the edges of G such that any two edges each incident with one distinct endpoint of a third …

Three edges e1, e2 and e3 in a graph G are consecutive if they form a path (in this order) or
a cycle of lengths three. An injective edge coloring of a graph G=(V, E) is a coloring c of the …

A k-independent set in a connected graph is a set of vertices such that any two vertices in
the set are at distance greater than k in the graph. The k-independence number of a graph …

We consider subexponential algorithms finding weighted homomorphisms from intersection
graphs of curves (string graphs) with n vertices to a fixed graph H. We provide a complete …

An injective coloring of a graph is a vertex coloring where two vertices have distinct colors if
a path of length two exists between them. In this paper some results on injective colorings of …

A (proper) colouring is acyclic, star, or injective if any two colour classes induce a forest, star
forest or disjoint union of vertices and edges, respectively. Hence, every injective colouring …