Dinitz Problem

Given any assignment of -element sets to the locations of a square array, is it always possible tofind a Partial Latin Square? The fact that such a Partial Latin Square can always be found for a array can be proven analytically, and techniques were developed which also proved the existence for and arrays. However, the general problem eluded solution until it was answered in the affirmative by Galvin in1993 using results of Janssen (1993ab) and F. Maffray.

References

Chetwynd, A. and Häggkvist, R. ``A Note on List-Colorings.'' J. Graph Th. 13, 87-95, 1989.

Cipra, B. ``Quite Easily Done.'' In What's Happening in the Mathematical Sciences 2, pp. 41-46, 1994.

Erdös, P.; Rubin, A.; and Taylor, H. ``Choosability in Graphs.'' Congr. Numer. 26, 125-157, 1979.

Häggkvist, R. ``Towards a Solution of the Dinitz Problem?'' Disc. Math. 75, 247-251, 1989.

Janssen, J. C. M. ``The Dinitz Problem Solved for Rectangles.'' Bull. Amer. Math. Soc. 29, 243-249, 1993a.

Janssen, J. C. M. Even and Odd Latin Squares. Ph.D. thesis. Lehigh University, 1993b.

Kahn, J. ``Recent Results on Some Not-So-Recent Hypergraph Matching and Covering Problems.'' Proceedings of the Conference on Extremal Problems for Finite Sets. Visegràd, Hungary, 1991.

Kahn, J. ``Coloring Nearly-Disjoint Hypergraphs with Colors.'' J. Combin. Th. Ser. A 59, 31-39, 1992.

• Local Group Theory
• Locally Convex Space
• Locally Finite Space
• Locally Pathwise-Connected Space
• Local Maximum
• Local Minimum
• Local Ring
• Local Subgroup
• Local Surface
• Loculus of Archimedes
• Locus
• Log
• Logarithm
• Logarithmically Convex Function
• Logarithmic Binomial Formula
• Logarithmic Binomial Theorem
• Logarithmic Distribution
• Logarithmic Integral
• Logarithmic Number
• Logarithmic Spiral
• Logarithmic Spiral Caustic Curve
• Logarithmic Spiral Evolute
• Logarithmic Spiral Inverse Curve
• Logarithmic Spiral Pedal Curve
• Logarithmic Spiral Radial Curve