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On some properties of 4‐regular plane graphs
Author(s) -
Horňá Mirko,
Jendroľ Stanislav
Publication year - 1995
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.3190200206
Subject(s) - combinatorics , mathematics , chromatic scale , plane (geometry) , graph , face (sociological concept) , planar graph , discrete mathematics , geometry , social science , sociology
The d ‐distance face chromatic number of a connected plane graph is the minimum number of colors in such a coloring of its faces that whenever two distinct faces are at the distance at most d , they receive distinct colors. We estimate 1‐distance chromatic number for connected 4‐regular plane graphs. We show that 0‐distance face chromatic number of any connected multi‐3‐gonal 4‐regular plane graphs is 4. © 1995, John Wiley & Sons, Inc.