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Edge‐face chromatic number and edge chromatic number of simple plane graphs
Author(s) -
Luo Rong,
Zhang CunQuan
Publication year - 2005
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.20077
Subject(s) - combinatorics , mathematics , chromatic scale , simple graph , graph , enhanced data rates for gsm evolution , plane (geometry) , edge coloring , discrete mathematics , graph power , geometry , computer science , line graph , artificial intelligence
Given a simple plane graph G , an edge‐face k ‐coloring of G is a function ϕ : E ( G ) ∪ F (G) → {1,…, k } such that, for any two adjacent or incident elements a , b ∈ E ( G ) ∪ F ( G ), ϕ( a ) ≠ ϕ( b ). Let χ e ( G ), χ ef ( G ), and Δ( G ) denote the edge chromatic number, the edge‐face chromatic number, and the maximum degree of G , respectively. In this paper, we prove that χ ef ( G ) = χ e ( G ) = Δ( G ) for any 2‐connected simple plane graph G with Δ ( G ) ≥ 24. © 2005 Wiley Periodicals, Inc. J Graph Theory