A complete solution to the directed Oberwolfach problem of order $2 \pmod{4}$ with cycles of even lengths
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908840462647296 |
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| author | Burgess, A. C. Danziger, P. H. Lacaze-Masmonteil, A. |
| author_facet | Burgess, A. C. Danziger, P. H. Lacaze-Masmonteil, A. |
| contents | The Oberwolfach problem asks for a $2$-factorization of the complete graph in which each $2$-factor is isomorphic to a specific factor $F$. Recently, this problem has been extended to directed graphs. In this case, the directed Oberwolfach problem asks for a directed 2-factorization of the complete symmetric digraph in which each directed $2$-factor is isomorphic to a specific directed factor $F$. In this paper, we consider the directed Oberwolfach problem with directed 2-factors comprised of cycles of even lengths. Specifically, we provide a complete solution to this particular case when the order of the complete symmetric digraph is congruent to 2 modulo 4. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_16888 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A complete solution to the directed Oberwolfach problem of order $2 \pmod{4}$ with cycles of even lengths Burgess, A. C. Danziger, P. H. Lacaze-Masmonteil, A. Combinatorics The Oberwolfach problem asks for a $2$-factorization of the complete graph in which each $2$-factor is isomorphic to a specific factor $F$. Recently, this problem has been extended to directed graphs. In this case, the directed Oberwolfach problem asks for a directed 2-factorization of the complete symmetric digraph in which each directed $2$-factor is isomorphic to a specific directed factor $F$. In this paper, we consider the directed Oberwolfach problem with directed 2-factors comprised of cycles of even lengths. Specifically, we provide a complete solution to this particular case when the order of the complete symmetric digraph is congruent to 2 modulo 4. |
| title | A complete solution to the directed Oberwolfach problem of order $2 \pmod{4}$ with cycles of even lengths |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2602.16888 |