Cohen-Macaulayness of bipartite graphs is investigated by several
mathematicians and has been characterized combinatorially. In this note, we
give some different combinatorial conditions for a bipartite graph which are
equal to Cohen-Macaulayness of the graphs. Conditions in the previous works are
depending on an appropriate ordering on vertices of the graph. The conditions
presented in this paper are not depending to any ordering. Finally, we present
a fast algorithm to check Cohen-Macaulayness of a given bipartite graph.Comment: 7 page