Yin–Busch–Ferrera–Hartke–Jacobsen–Kaul–West degree-sequence packing conjecture

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Let n≥3n\ge 3 be an integer, and let (d11,…,dn1)(d_1^1,\ldots,d_n^1) and (d12,…,dn2)(d_1^2,\ldots,d_n^2) be graphic sequences with dn1,dn2≥1d_n^1,d_n^2\ge 1. Two graphic sequences pack when there are edge-disjoint graphs on the same labelled vertex set realizing them. Yin–Busch–Ferrera–Hartke–Jacobsen–Kaul–West packing conjecture. If

d11d12<n2,d_1^1d_1^2<\frac{n}{2},

then (d11,…,dn1)(d_1^1,\ldots,d_n^1) and (d12,…,dn2)(d_1^2,\ldots,d_n^2) pack. The paper states that this conjecture is fully verified, so the asserted result is a theorem rather than an open conjecture.

References

Primary source

Joseph Briggs, Jessica McDonald and Songling Shan, “Degree sequences realizing labelled perfect matchings”, arXiv:2510.01110 (2025).

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