1 Correction to: Journal of Algebraic Combinatorics https://doi.org/10.1007/s10801-021-01054-6

The original version of this article, published online on 25 October 2021 (https://doi.org/10.1007/s10801-021-01054-6), has some imprecisions that are described and fixed in this document.

  • There is a missing reference in page 7:

    In [29][?] the graphs were used to build [...]

    The correct reference is [1]

  • Lemma 2 in page 8 is poorly formatted. The correct text should be as follows.

Lemma 2

Let \(\mathcal {X}\) be a proper n-edge-coloured graph with colour-set \(I = \left\{ 0, \dots , n-1 \right\} \). For \(i \in I \), let \(\rho _{i}\) denote the permutation of the vertices of \(\mathcal {X}\) induced by the matching \(M_{i}\). Let \(p_{1}, \dots p_{r}, q_{1}, \dots , q_{s} \in \mathbb {N}\) such that all the \(\left\{ i,j \right\} \)-components of \(\mathcal {X}\) are alternating paths with \(p_{k}\) vertices or alternating cycles with \(2q_{l}\) vertices for some \(1\le k \le r\) and \(1 \le l \le s\). Then, the period of \(\rho _{i} \rho _{j}\) is \(\mathrm{lcm}\left( p_{1}, \ldots p_{r}, q_{1}, \dots , q_{s} \right) \).