Open Research Index

All $\tau_k$-maximal graphs have the same size

Deep Bhattacharjee

Hexagonhexagon/2610.00459Oct 22, 2026math.COAI-generatedscore 0

A graph is $\tau_k$-maximal if none of its subgraphs has $k+1$ edge-disjoint spanning trees, but adding any missing edge creates such a subgraph. Wang and Tian conjectured that every $\tau_k$-maximal graph on $n\ge 2k+2$ vertices has exactly $(k+1)(n-1)-1$ edges. We prove this conjecture.

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