It is proved in this paper that every bipartite graphic sequence with the minimum degree
2 has a realization that admits a nowhere-zero 4-flow. This result implies a conjecture originally proposed by Keedwell (1993) and reproposed by Cameron (1999) about simultaneous edge-colorings and critical partial Latin squares.
Mathematics Subject Classification (2000):
05C15 - 05B15 - 05C38 - 05C70 - 05C07
* Partially supported by RGC grant HKU7054/03P.
Partially supported by the National Security Agency under Grants MDA904-00-1-00614 and MDA904-01-1-0022.