Sciweavers

COMBINATORICS
2002

Graph Color Extensions: When Hadwiger's Conjecture and Embeddings Help

13 years 3 months ago
Graph Color Extensions: When Hadwiger's Conjecture and Embeddings Help
Suppose G is r-colorable and P V (G) is such that the components of G[P] are far apart. We show that any (r + s)-coloring of G[P] in which each component is s-colored extends to an (r + s)-coloring of G. If G does not contract to K5 or is planar and s 2, then any (r + s - 1)-coloring of P in which each component is s-colored extends to an (r + s - 1)-coloring of G. This result uses the Four Color Theorem and its equivalence to Hadwiger's Conjecture for k = 5. For s = 2 this provides an affirmative answer to a question of Thomassen. Similar results hold for coloring arbitrary graphs embedded in both orientable and non-orientable surfaces.
Michael O. Albertson, Joan P. Hutchinson
Added 17 Dec 2010
Updated 17 Dec 2010
Type Journal
Year 2002
Where COMBINATORICS
Authors Michael O. Albertson, Joan P. Hutchinson
Comments (0)