Cyclic matching sequencibility of graphs

@article{Brualdi2011CyclicMS,
  title={Cyclic matching sequencibility of graphs},
  author={Richard A. Brualdi and Kathleen Kiernan and Seth A. Meyer and Michael W. Schroeder},
  journal={Australasian J. Combinatorics},
  year={2011},
  volume={53},
  pages={245-256}
}
We define the cyclic matching sequencibility of a graph to be the largest integer $d$ such that there exists a cyclic ordering of its edges so that every $d$ consecutive edges in the cyclic ordering form a matching. We show that the cyclic matching sequencibility of $K_{2m}$ and $K_{2m+1}$ equal $m-1$. 

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