Two Graphs Without Planar Covers

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