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Plane graphs of maximum degree Δ ≥ 7 are edge‐face (Δ + 1)‐colorable
Author(s) -
Wang Yiqiao,
Hu Xiaoxue,
Wang Weifan,
Lih KoWei
Publication year - 2020
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.22538
Subject(s) - combinatorics , mathematics , plane (geometry) , enhanced data rates for gsm evolution , graph , degree (music) , planar graph , face (sociological concept) , edge coloring , discrete mathematics , geometry , graph power , computer science , line graph , physics , artificial intelligence , sociology , acoustics , social science
A plane graph G is edge‐face k ‐colorable if its edges and faces can be colored with k colors such that any two adjacent or incident elements receive different colors. It is known that every plane graph G of maximum degree Δ ≥ 8 is edge‐face (Δ + 1)‐colorable. The condition Δ ≥ 8 is improved to Δ ≥ 7 in this paper.