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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.18253 |
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| _version_ | 1866915873838596096 |
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| author | Bogdanov, Ilya I. Petrov, Fedor Sadovnichiy, Anton Ushakov, Fedor |
| author_facet | Bogdanov, Ilya I. Petrov, Fedor Sadovnichiy, Anton Ushakov, Fedor |
| contents | In 2019, P. Higgins formulated [1] a question about bipartite graphs (see Conjecture 1 below); this question arises in the study of regular finite semigroups. F. V. Petrov formulated [2] another combinatorial conjecture (Conjecture 3); Conjecture 3 implies Conjecture 1 and seems simple itself. However, both conjectures remain unproven in the general case. In the present paper, some special cases are proved, Conjecture 4 is formulated in the same spirit, and some of its special cases are proved. In addition, Conjecture 1 is reduced to a matrix inequality (Conjecture 5); this inequality is, in turn, also proved in a special case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_18253 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Biregular bipartite labeled multigraphs and perfect matchings in bipartite tensor products Bogdanov, Ilya I. Petrov, Fedor Sadovnichiy, Anton Ushakov, Fedor Combinatorics In 2019, P. Higgins formulated [1] a question about bipartite graphs (see Conjecture 1 below); this question arises in the study of regular finite semigroups. F. V. Petrov formulated [2] another combinatorial conjecture (Conjecture 3); Conjecture 3 implies Conjecture 1 and seems simple itself. However, both conjectures remain unproven in the general case. In the present paper, some special cases are proved, Conjecture 4 is formulated in the same spirit, and some of its special cases are proved. In addition, Conjecture 1 is reduced to a matrix inequality (Conjecture 5); this inequality is, in turn, also proved in a special case. |
| title | Biregular bipartite labeled multigraphs and perfect matchings in bipartite tensor products |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2603.18253 |