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A conjecture of Borodin and a coloring of Grünbaum
Author(s) -
Rautenbach Dieter
Publication year - 2008
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.20299
Subject(s) - combinatorics , mathematics , graph coloring , conjecture , list coloring , graph , complete coloring , planar graph , fractional coloring , edge coloring , discrete mathematics , graph power , line graph
In 1976, Borodin conjectured that every planar graph has a 5‐coloring such that the union of every k color classes with 1 ≤ k ≤ 4 induces a ( k —1)‐degenerate graph. We prove the existence of such a coloring using 18 colors. © 2008 Wiley Periodicals, Inc. J Graph Theory 58:139–147, 2008
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