Jan 25, 2005 · Title:Coloring graphs with crossings ... Abstract: We generalize the Five Color Theorem by showing that it extends to graphs with two crossings.

May 6, 2009 · Furthermore, we show that if a graph has three crossings, but does not contain K 6 as a subgraph, then it is also 5-colorable.

Jan 19, 2005 · We generalize the Five Color Theorem by showing that it extends to graphs with two crossings. Furthermore, we show that if a graph has three ...

If χ(G) = k then G contains a k-critical subgraph. Algorithm for k colorability of G. • let K be all (k + 1)-critical graphs.

The famous Four Color Theorem [4, 23] asserts that every graph that can be drawn in the plane with no crossings is 4-colorable. It is natural to ask what number ...

May 6, 2009 · The crossing number of a graph G, denoted by ν(G), is the minimum number of crossings in a drawing of G. An optimal drawing of G is a drawing of ...

However, we show that every graph with crossing number at most 4 and clique number at most 5 is 5-colorable. We also show some colorability results on graphs ...

We show that every graph with two crossings is 5-choosable. We also prove that every graph which can be made planar by removing one edge is 5-choosable.

Albertson conjectured that if graph G has chromatic number r, then the crossing number of G is at least that of the complete graph Kr. This conjecture in the ...