Summary: Two Graphs
Without Planar Covers
Dept. of Math. and Stat.
University of Vermont
Burlington, VT, USA 05405
August 13, 2001 (after referee reports)
In this note we prove that two specic 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 specic
graphs do not have nite planar covers. Previous (and subsequent)
work has reduced these 103 to a few specic 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.
The purpose of this paper is to prove that two specic graphs do not have