It is proved that there is a function f : N N such that the following holds. Let G be a graph embedded in a surface of Euler genus g with all faces of even size and with edge-wid...
A simple characterization of the 3, 4, or 5-colorable Eulerian triangulations of the projective plane is given. Key words: Projective plane, triangulation, coloring, Eulerian grap...
Let G = (V, E) be a graph. Let c : V → N be a vertex-coloring of the vertices of G. For any vertex u, we denote by N[u] its closed neighborhood (u and its adjacent vertices), an...
Attempts to solve the famous Four Color Problem led to fruitful discoveries and rich coloring theories. In this talk, some old and some recent applications of tools from topology ...
In [13], Erd˝os et al. defined the local chromatic number of a graph as the minimum number of colors that must appear within distance 1 of a vertex. For any ∆ ≥ 2, there are ...