Wagner’s network-found tree refutes Collins’s peak-position conjecture
- Mathematics
The selected contribution is the 48-vertex tree of §2.4, not Wagner’s subsequent infinite-family theorem.
Collins's tree-polynomial peak conjecture
- Mathematics
Collins conjectured that the nonzero adjacency-polynomial coefficients of a tree peak at the same normalized position as its normalized distance-polynomial coefficients.
Curated contributions 1
Understand the problem ↓Understanding the problem
Read the background
Collins conjectured that the nonzero adjacency-polynomial coefficients of a tree peak at the same normalized position as its normalized distance-polynomial coefficients. Wagner reports a network-found 48-vertex tree whose peak ratios are 1/7 and 1/2, respectively.
Why it matters
The finite tree provides a concrete counterexample; Wagner's later infinite-family argument is a separate human derivation informed by it.
What counts as progress
Is there a tree for which the normalized adjacency and distance characteristic-polynomial coefficient peaks occur at different positions?
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