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On possible counterexamples to Negami's planar cover conjecture

dc.contributor.authorHliněný, Petr
dc.contributor.authorThomas, Robin
dc.date.accessioned2006-10-11T15:13:50Z
dc.date.available2006-10-11T15:13:50Z
dc.date.issued2004
dc.identifier.citationJournal of Graph Theory. 2004, vol. 46, issue 3, p. 183-206.en
dc.identifier.issn0364-9024
dc.identifier.issn1097-0118
dc.identifier.urihttp://hdl.handle.net/10084/57054
dc.language.isoenen
dc.publisherWileyen
dc.relation.ispartofseriesJournal of Graph Theoryen
dc.relation.urihttps://doi.org/10.1002/jgt.10177en
dc.subjectgraphen
dc.subjectplanar coveren
dc.subjectprojective planeen
dc.subjectminoren
dc.titleOn possible counterexamples to Negami's planar cover conjectureen
dc.typearticleen
dc.identifier.locationNení ve fondu ÚKen
dc.description.abstract-enA simple graph H is a cover of a graph G if there exists a mapping phi from H onto G such that phi maps the neighbors of every vertex v in H bijectively to the neighbors of phi(v) in G. Negami conjectured in 1986 that a connected graph has a finite planar cover if and only if it embeds in the projective plane. The conjecture is still open. It follows from the results of Archdeacon, Fellows, Negami, and the first author that the conjecture holds as long as the graph K-1,K-2,K-2,K-2 has no finite planar cover. However, those results seem to say little about counterexamples if the conjecture was not true. We show that there are, up to obvious constructions, at most 16 possible counterexamples to Negami's conjecture. Moreover, we exhibit a finite list of sets of graphs such that the set of excluded minors for the property of having finite planar cover is one of the sets in our list.
dc.identifier.doi10.1002/jgt.10177
dc.identifier.wos000222120100004


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