On the Completion of Partial Latin SquaresSchool of Operations Research and Industrial Engineering, College of Engineering, Cornell University, 1977 - Magic squares - 172 pages |
Contents
NECESSARY CONDITION I | 12 |
CHAPTER III | 33 |
RELATIONS AMONG NECESSARY CONDITIONS | 46 |
Copyright | |
3 other sections not shown
Common terms and phrases
2k H cell i,j combinatorial complete bipartite graph condition II.2.1 conjunctive normal form consisting Corollary corresponding network CPLS D₁ define denote the set doubly stochastic matrix edge i,j edge set edges E(k Edmonds and Fulkerson equivalent exact cover exists flow decomposition following theorem Fulkerson 1965 Given a PLS graph G Hence illustrated in Figure independent sets integers K₁ K₂ L-type PLS Lemma linear programming M₂ matroid condition max-flow min-cut theorem maximal flow necessary and sufficient necessary condition network condition network flow network G node sets nondeterministic algorithm nonnegative NP-complete nxn PLS occupied by symbol partial latin square partition matroids perfect matching permutation preassigned Proof respectively S₁ set of edges set of rows Sijk strongly-base-orderable subnetwork subset sufficient condition Theorem III.1.2 timetabling problem transversal matroid triply stochastic matrix unoccupied cells V₁ violating set Xijk кек кеко