# Coloring Number Of Planar Graphs

**We show that the game coloring number of a planar graph is at most 19.**

**Coloring number of planar graphs**.
Hence col g P 4 13.
And now here is the initial photograph.
The famous fourcolor theorem proved in 1976 says that the vertices of any planar graph can be colored in four colors so that adjacent vertices receive different colors Kempes method of 1879 despite falling short of being a proof does lead to a good algorithm for fourcoloring planar graphs The method is recursive One finds a vertex that has degree at most 5 such exists by Eulers formula for.

Planar graph so the same diﬃculty is true for planar graphs with smaller chromatic number. S f12kgsuch that 8uw2V if uw 2E then fu 6 fw. Illinois Journal of Mathematics 1977.

If G is a planar graph with girth at least 4 then col g G 13. Every Planar Map is Four Colorable Part II. We will construct L as follows.

JO - Journal für die reine und angewandte Mathematik PY - 1989 VL - 394 SP - 180 EP - 185 KW - total chromatic number. Free Printable Coloring Pages. Chromatic number of a graph.

Journal of Combinatorial Optimization 361 55-64. The inequality above shows that any planar graph is 5 -degenerate and a similar inductive argument shows that all k -degenerate graphs are k 1 -colorable. Illinois Journal of Mathematics 1977.

This problem was first posed in the nineteenth century and it was quickly conjectured that in all cases four colors suffice. The following color assignment satisfies the coloring constraint Red. This paper discusses a variation of the game chromatic number of a graph.