This paper is a sequel of our previous paper (N. Kita: Bipartite graft {II}: Cathedral decomposition for combs. arXiv preprint arXiv:2101.06678, 2021). In our previous paper, a graft analogue of the Dulmage-Mendelsohn decomposition has been introduced for comb bipartite grafts. In this paper, we prove how this result can be extended for general bipartite grafts.
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