Cubic graphs – those regular ... Equitable Total Colouring: A colouring method where both vertices and edges are coloured in such a way that the numbers of elements per colour differ by at most one.

Chapter 6 We say that a graph G covers a graph H if there exists a map f: V(G) –> V(H) such that f is onto and for any vertex v of G, the restriction of f to N(v) is a bijection to N(f(v)).For example ...

Let us say that a graph is k-apex if it contains a set of at most k vertices whose removal yields a planar graph. We define the apex number of a graph G as the minimum k for which G is k-apex. ... It ...

For example, sudoku is a graph-coloring problem in disguise. View each cell as a vertex and the nine digits as the colors. Each vertex has 20 edges coming out of it — one to each cell in its row, in ...