n -Tuple Coloring of Planar Graphs with Large Odd Girth | Zendy

William F. Klostermeyer | Zendy; Cun Quan Zhang | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

n -Tuple Coloring of Planar Graphs with Large Odd Girth

Author(s) -

William F. Klostermeyer,

Cun Quan Zhang

Publication year - 2002

Publication title -

graphs and combinatorics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.59

H-Index - 40

eISSN - 1435-5914

pISSN - 0911-0119

DOI - 10.1007/s003730200007

Subject(s) - combinatorics , mathematics , odd graph , planar graph , graph homomorphism , outerplanar graph , discrete mathematics , graph power , triangle free graph , butterfly graph , wheel graph , graph , vertex (graph theory) , 1 planar graph , line graph , pathwidth , voltage graph

. The main result of the papzer is that any planar graph with odd girth at least 10k−7 has a homomorphism to the Kneser graph G k 2 k +1, i.e. each vertex can be colored with k colors from the set {1,2,…,2k+1} so that adjacent vertices have no colors in common. Thus, for example, if the odd girth of a planar graph is at least 13, then the graph has a homomorphism to G 2 5, also known as the Petersen graph. Other similar results for planar graphs are also obtained with better bounds and additional restrictions.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research