In this chapter G=(V, E) denotes an arbitrary undirected graph without loops, where V={v 1, v
2,…, vn} is its vertex set and E={e 1, e 2,…, em}⊂(E× E) is its edge set. Two edges are …

Graphs can be represented in many di erent ways: by lists of edges, by incidence relations,
by adjacency matrices, and by other similar structures. These representations are well suited …

On the 1-chromatic number of nonorientable surfaces with large genus Page 1 Journal of
Combinatorial Theory, Series B 102 (2012) 283–328 Contents lists available at SciVerse …

The 1-chromatic numberχ1 (S) of a surfaceSis the maximum chromatic number of all graphs
which can be drawn on the surface so that each edge is crossed by no more than one other …

Let χ1 (S) be the maximum chromatic number for all graphs which can be drawn on a
surface S so that each edge is crossed by no more than one other edge. It is proved that if 2 …

Let χ1 (S) be the maximum chromatic number for all graphs which can be drawn on a
surface S so that each edge is crossed over by no more than one other edge. In the previous …

The 1-genus of a graph is the smallest possible genus of an orientable surface such that the
graph can be drawn on the surface so that each edge is crossed over by no more than one …

The vertex-face chromatic number of a map on a surface is the minimum integer m such that
the vertices and faces of the map can be colored by m colors in such a way that adjacent or …