Projective plane graphs and 3-rigidity

2020/03/11 by Kastis, Eleftherios, Power, Stephen · 1 citation
#52C25 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2003.05514

Abstract

It is shown that a simple graph which is embeddable in the real projective plane is minimally 3-rigid if and only if it is (3,6)-tight. Moreover the topologically uncontractible embedded graphs of this type are constructible from one of 8 embedded graphs by a sequence of vertex splitting moves. In particular the characterisation of minimal 3-rigidity holds for a triangulated Mobius strip.

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