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Rank‐width is less than or equal to branch‐width
Author(s) -
Oum Sangil
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.20280
Subject(s) - mathematics , combinatorics , graph , factor critical graph , cubic graph , rank (graph theory) , discrete mathematics , voltage graph , line graph
We prove that the rank‐width of the incidence graph of a graph G is either equal to or exactly one less than the branch‐width of G , unless the maximum degree of G is 0 or 1. This implies that rank‐width of a graph is less than or equal to branch‐width of the graph unless the branch‐width is 0. Moreover, this inequality is tight. © 2007 Wiley Periodicals, Inc. J Graph Theory 57: 239–244, 2008
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