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On stable crossing numbers
Author(s) -
Kainen Paul C.,
White Arthur T.
Publication year - 1978
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.3190020302
Subject(s) - mathematics , combinatorics , bipartite graph , generalization , cartesian product , crossing number (knot theory) , discrete mathematics , graph , mathematical analysis , intersection (aeronautics) , engineering , aerospace engineering
Results giving the exact crossing number of an infinite family of graphs on some surface are very scarce. In this paper we show the following: for G = Q n × K 4.4 , cr y ( G )‐ m ( G ) = 4 m , for 0 ⩽ = m ⩽ 2 n . A generalization is obtained, for certain repeated cartesian products of bipartite graphs. Nonorientable analogs are also developed.