## 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