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Blocks and the nonorientable genus of graphs
Author(s) -
Stahl Saul,
Beineke Lowell W.
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.3190010114
Subject(s) - mathematics , combinatorics , counterexample , genus , graph , discrete mathematics , botany , biology
Examples are given to show that the nonorientable genus of a graph is not additive over its blocks. A nonorientable analog for the Battle, Harary, Kodama, and Youngs Theorem is proved; this completely determines the nonorientable genus of a graph in terms of its blocks. It is also shown that one of the above counterexamples has the minimum possible order.