20 Years of Negami's Planar Cover Conjecture

In 1988, Seiya Negami published a conjecture stating that a graph G has a finite planar cover (i.e. a homomorphism from some planar graph onto G which maps the vertex neighbourhoods bijectively) if and only if G embeds in the projective plane. Though the ”if” direction is easy, and over ten related research papers have been published during the past 20 years of investigation, this beautiful conjecture is still open in 2008. We give a short accessible survey on Negami’s conjecture and all the (so far) published partial results, and outline some further ideas to stimulate future research towards solving the conjecture. Key words. graph cover; graph homomorphism, projective graphs

• Type: Journal
• Year: 2010
• Where: GC
• Authors: Petr Hlinený
• Keywords: Applied Computing, Conjecture, GC 2010, Planar Graph, finite Planar