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NECESSARY CONDITION I
NECESSARY CONDITION II
RELATIONSAMONG NECESSARY CONDITIONS
3 other sections not shown
assignment of symbol characteristic matrix color combinatorial complete bipartite graph condition II.2.1 conjunctive normal form consisting Corollary corresponding network CPLS define Deleting the edges denote the set doubly stochastic matrix edge i,j edge set edges E(k Edmonds and Fulkerson equivalent exact cover flow decomposition following theorem Fulkerson 1965 Given a PLS graph G Hence illustrated in Figure independent sets Jq x Kq L-type PLS latin rectangle linear programming magic squares matroid condition max H max-flow min-cut theorem maximal flow necessary and sufficient necessary condition network condition network flow network G node sets nondeterministic algorithm NP-complete nxn PLS occupied by symbol P(IQ x Jq partial latin square partition matroids perfect matching permutation preassigned Proof relation respectively set of edges set of rows solution strongly-base-orderable subnetwork subset ACE sufficient condition Theorem II.4.1 Theorem III.1.2 timetabling problem transversal matroid triply stochastic matrix violating set