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Degree Sequences vs. Forests in Bipartite Graphs
Darij Grinberg, Benjamin Liber · 2026-03-03 · via math updates on arXiv.org

We prove a conjecture of Shteiner and Shteyner stating that for a bipartite graph $G=(V,E)$, the number of forests in $G$ equals the number of degree sequences arising from its spanning subgraphs. In the process, we provide several equivalent evaluations of the Tutte polynomial $T_G(x,y)$ at $(2,1)$, including interpretations in terms of degree vectors obtained from orientations of $G$.