Regular matchstick graphs on the sphere

2025/02/12 by Swanepoel, Konrad J.
#05C10 #52C10 #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2502.08294

Abstract

We show that the 5-regular matchstick graphs on the sphere are exactly the five 5-regular contact graphs of congruent caps on the sphere found by R. M. Robinson (1969).

Related

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• No finite 5-regular matchstick graph exists
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