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Vertex signatures and edge‐4‐colorings of 4‐regular plane graphs
Author(s) -
Jaeger François,
Koester Gerhard
Publication year - 1990
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.3190140402
Subject(s) - combinatorics , mathematics , corollary , vertex (graph theory) , disjoint sets , discrete mathematics , graph
We associate partitions of the edge‐set of a 4‐regular plane graph into 1‐factors or 2‐factors to certain 3‐valued vertex signatures in the spirit of the work by H. Grötzsch [1]. As a corollary we obtain a simple proof of a result of F. Jaeger and H. Shank [2] on the edge‐4‐colorability of 4‐regular plane graphs made up by the superposition of 4 families of disjoint simple closed curves.