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Summary: Two Graphs
Without Planar Covers
Dan Archdeacon
Dept. of Math. and Stat.
University of Vermont
Burlington, VT, USA 05405
e-mail: dan.archdeacon@uvm.edu
August 13, 2001 (after referee reports)
Abstract
In this note we prove that two speci c graphs do not have nite
planar covers. The graphs are K 7 C 4 and K 4;5 4K 2 . This research
is related to Negami's 1-2-1 Conjecture which states \A graph G has
a nite planar cover if and only if it embeds in the projective plane".
In particular, Negami's conjecture reduces to showing that 103 speci c
graphs do not have nite planar covers. Previous (and subsequent)
work has reduced these 103 to a few speci c graphs. This paper covers
2 of the remaining cases. The sole case currently remaining is to show
that K 2;2;2;1 has no nite planar cover.
1 Introduction
The purpose of this paper is to prove that two speci c graphs do not have
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