Bipartite Graft III: General Case

TL;DR

This paper extends a bipartite graft decomposition technique from special comb structures to general bipartite grafts, broadening the applicability of the original method.

Contribution

It generalizes the bipartite graft decomposition from comb structures to all bipartite grafts, advancing the theoretical framework.

Findings

Extended the decomposition to general bipartite grafts

Provided a unified framework for bipartite graft analysis

Enhanced understanding of bipartite graft structure

Abstract

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.