Completing Multi‐Latin Rectangles via Factors With Prescribed Degrees in Bipartite Graphs

ABSTRACT Let be an array whose top left sub‐array is filled with a set of different symbols such that each cell of contains symbols. In this note, we find conditions under which each empty cell of can be filled with symbols in such a way that the total number of occurrences of each symbol is prescribed and that each symbol occurs at most times in each row and column of . To prove this result, we establish a new criterion for a bipartite graph to have a subgraph with prescribed degree conditions. Our proof is self‐contained and relies on the alternating path technique.