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On Planar Hypohamiltonian Graphs

Wiener, Gabor; Araya, Makoto


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    <subfield code="a">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 &amp;gt;= N there exists a planar hypohamiltonian/hypotraceable graph on n vertices. (C) 2010 Wiley Periodicals, Inc. J Graph Theory 67: 55-68, 2011</subfield>
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