| Abstract: | In this note we prove that two specific graphs do not have finite planar covers. The graphs are K7–C4 and K4,5–4K2. This research is related to Negami's 1‐2‐∞ Conjecture which states “A graph G has a finite planar cover if and only if it embeds in the projective plane.” In particular, Negami's Conjecture reduces to showing that 103 specific graphs do not have finite planar covers. Previous (and subsequent) work has reduced these 103 to a few specific graphs. This paper covers 2 of the remaining cases. The sole case currently remaining is to show that K2,2,2,1 has no finite planar cover. © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 318–326, 2002 |
