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New proof demonstrates the min-max relation for f-bounded subgraphs, suggesting broader applications in combinatorial optimization.
Given a nonnegative integer weight for each vertex in a multigraph , an ‐bounded subgraph of is a multigraph contained in such that for all . Using Tutte's ‐Factor Theorem, we give a new proof of the min–max relation for the maximum size of an ‐bounded subgraph of . When for all , the formula reduces to the classical Tutte–Berge Formula for the maximum size of a matching.
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Qu et al. (2026) studied this question.
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