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The biparticity of a graph
Author(s) -
Harary Frank,
Hsu Derbiau,
Miller Zevi
Publication year - 1977
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.3190010208
Subject(s) - combinatorics , mathematics , edge transitive graph , outerplanar graph , graph minor , planar graph , bipartite graph , graph , graph power , discrete mathematics , line graph , voltage graph
The biparticity β( G ) of a graph G is the minimum number of bipartite graphs required to cover G . It is proved that for any graph G , β( G ) = {log 2 χ( G )}. In view of the recent announcement of the Four Color Theorem, it follows that the biparticity of every planar graph is 2.