Nowhere-Zero 4-Flows, Simultaneous Edge-Colorings, And Critical Partial Latin Squares

It is proved in this paper that every bipartite graphic sequence with the minimum degree δ ≥ 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.

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Correspondence to Rong Luo.

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* 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.

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Luo, R., Zang*, W. & Zhang†, CQ. Nowhere-Zero 4-Flows, Simultaneous Edge-Colorings, And Critical Partial Latin Squares. Combinatorica 24, 641–657 (2004). https://doi.org/10.1007/s00493-004-0039-2

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Mathematics Subject Classification (2000):

  • 05C15
  • 05B15
  • 05C38
  • 05C70
  • 05C07