5-factor-critical graphs on the torus
Quan‐Lin Li, Heping Zhang · Lanzhou University Institutional Repository · 2014
A graph of order n is said to be k-factor-critical for non-negative integer k <= n if the removal of any k vertices results in a graph with a perfect matching. For a k-factor-critical graph of order n, it is called trivial if k = n and non-trivial otherwise. It is known that the toroidal graphs are at most non-trivial 5-factor-critical. Motivated by this, we are to characterize all non-trivial 5-factor-critical graphs on the torus in this paper.