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Alternating cycles in edge‐colored graphs
Author(s) -
Whitehead Carol
Publication year - 1989
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.3190130402
Subject(s) - combinatorics , mathematics , vertex (graph theory) , colored , graph , edge coloring , multiple edges , 1 planar graph , discrete mathematics , line graph , graph power , materials science , composite material
We show that the edges of a 2‐connected graph can be partitioned into two color classes so that every vertex is incident with edges of each color and every alternating cycle passes through a single edge. We also show that the edges of a simple graph with minimum vertex degree δ ≫ 2 can be partitioned into three color classes so that every vertex is incident with edges in exactly two colors and no cycle is alternating.