A Short Proof of Ore’s f-Factor Theorem Using Flows

Abstract

AbstractThe existence of a spanning subgraph with a prescribed degree sequence in a bipartite graph has been characterized by Ore, called Ore’s f-factor theorem. In this paper, we prove Ore’s theorem using flows in networks and our proof is simpler. A polynomial time (linear) algorithm \(O(n+m)\) is derived to find an f-factor if it exists or else a succinct certificate is found to prove the non-existence of an f-factor. The deficiency version of Ore’s theorem is given.