On the structure of minimally n-extendable bipartite graphs Original Research Article

It is proved that, in a minimal n-extendable bipartite graph, the subgraph induced by the edges both ends of which have degree at least n + 2 is a forest. As a consequence, every minimal n-extendable bipartite graph has at least 2n + 2 vertices of degree n + 1. This result is sharp. Some other structural results on minimally n-extendable bipartite graphs are also given.