Corrigendum to "Paths and circuits in finite groups", Discr. Math. 22 (1978) 263

TL;DR

This paper corrects and clarifies previous results on prime partitionable numbers, establishing equivalences among different definitions and relating them to Erdos-Woods numbers.

Contribution

It removes a specific number from the set of prime partitionable numbers and proves the equivalence of various definitions and related number sets.

Findings

52 is not prime partitionable

Two definitions of prime partitionable numbers are equivalent

Prime partitionable numbers are equivalent to Erdos-Woods numbers

Abstract

We remove 52 from the set of prime partitionable numbers in a paper by Holsztynski and Strube (1978), which also appears in a paper by Erdos and Trotter in the same year. We establish equivalence between two different definitions in the two papers, and further equivalence to the set of Erdos-Woods numbers.