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- Title
Circular Coloring of Planar Digraphs.
- Authors
Wang, Guanghui; Liu, Bin; Yu, Jiguo; Liu, Guizhen
- Abstract
Let D be a digraph. The circular chromatic number $${\chi_c(D)}$$ and chromatic number $${\chi(D)}$$ of D were proposed recently by Bokal et al. Let $${\vec{\chi_c}(G)={\rm max}\{\chi_c(D)| D\, {\rm is\, an\, orientation\, of} G\}}$$. Let G be a planar graph and n ≥ 2. We prove that if the girth of G is at least $${\frac{10n-5}{3},}$$ then $${\vec{\chi_c}(G)\leq \frac{n}{n-1}}$$. We also study the circular chromatic number of some special planar digraphs.
- Subjects
GRAPH coloring; DIRECTED graphs; GRAPH theory; PROOF theory; COMBINATORICS; HOMOMORPHISMS
- Publication
Graphs & Combinatorics, 2012, Vol 28, Issue 6, p889
- ISSN
0911-0119
- Publication type
Article
- DOI
10.1007/s00373-011-1084-4