Abstract:It has been conjectured that the minimum and maximum of the mean subtree order among connected graphs of order $n$ are attained by the path $P_n$ and clique $K_n$, respectively. Extending ideas due to Haslegrave and Vince, we confirm that the minimum is indeed attained by $P_n$. We also show that the maximum is attained by $K_n$ by proving that the ratio between spanning and almost spanning trees is maximised by the clique and applying a double-counting argument.
From: Stijn Cambie [view email]
[v1]
Thu, 28 Aug 2025 09:32:12 UTC (21 KB)
[v2]
Wed, 16 Sep 2026 18:38:54 UTC (25 KB)
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