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Regular graphs in which every pair of points is missed by some longest cycle. (English) Zbl 1174.05419
Summary: In Petersen’s well-known cubic graph every vertex is missed by some longest cycle. Thomassen produced a planar graph with this property. Grünbaum found a cubic graph, in which any two vertices are missed by some longest cycle. In this paper we present a cubic planar graph fulfilling this condition.
##### MSC:
 05C38 Paths and cycles
##### Keywords:
Planar; cubic; $$3$$-connected; graph