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On planar hypohamiltonian graphs
Author(s) -
Wiener Gábor,
Araya Makoto
Publication year - 2011
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.20513
Subject(s) - combinatorics , mathematics , planar graph , corollary , wheel graph , outerplanar graph , discrete mathematics , graph , book embedding , graph power , 1 planar graph , chordal graph , pathwidth , line graph
We present a planar hypohamiltonian graph on 42 vertices and (as a corollary) a planar hypotraceable graph on 162 vertices, improving the bounds of Zamfirescu and Zamfirescu and show some other consequences. We also settle the open problem whether there exists a positive integer N , such that for every integer n ≥ N there exists a planar hypohamiltonian/hypotraceable graph on n vertices. © 2010 Wiley Periodicals, Inc. J Graph Theory 67: 55‐68, 2011
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