Coverings of transfinite matrices

Mordecai Lewin
1974 Journal of combinatorial theory. Series A  
Subsets of a Cartesian product X x Y, where X and Y are arbitrary sets, are considered as a generalization of incidence matrices. Minimal cover, essential set etc. are introduced in a stronger sense and their properties discussed. The existence of a minimal cover for an arbitrary generalized incidence matrix is proved. As an application a previous result is extended. This theorem is a consequence of the canonical form for bipartite graphs offinite exterior dimension (in the language of
more » ... a matrix which admits of a finite cover) established by Dulmage and Mendelsohn in [3] and of Theorem 3.1 and what follows, in Brualdi's paper [l]. See also [4] , where this theorem is proved independently. 131
doi:10.1016/0097-3165(74)90039-9 fatcat:h5nac3rqx5cgbofkujegb7u43e