How not to characterize planar-emulable graphs
IWOCA'11 Proceedings of the 22nd international conference on Combinatorial Algorithms
On the complexity of planar covering of small graphs
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
Locally constrained graph homomorphisms-structure, complexity, and applications
Computer Science Review
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A simple graph H is a cover of a graphG if there exists a mapping Φ fromH onto G such that Φ maps theneighbors of every vertex υ in H bijectivelyto the neighbors of Φ (ν) in G. Negamiconjectured in 1986 that a connected graph has a finite planarcover if and only if it embeds in the projective plane. Theconjecture is still open. It follows from the results ofArchdeacon, Fellows, Negami, and the first author that theconjecture holds as long as the graphK1,2,2,2 has no finite planar cover.However, those results seem to say little about counterexamples ifthe conjecture was not true. We show that there are, up to obviousconstructions, at most 16 possible counterexamples to Negami'sconjecture. Moreover, we exhibit a finite list of sets of graphssuch that the set of excluded minors for the property of havingfinite planar cover is one of the sets in our list. © 2004Wiley Periodicals, Inc. J Graph Theory 46: 183206, 2004