MathDB

WOWII Graph Conjecture 36

The supplied source identifies this as a conjecture about finite graphs, with the relevant configuration involving a connected graph GG of radius 33 having exactly one diametrical pair, i.e. ∣{{u,v}⊆V(G):dG(u,v)=diam⁡(G)}∣=1\left|\left\{\{u,v\}\subseteq V(G):d_G(u,v)=\operatorname{diam}(G)\right\}\right|=1. The conjecture’s full conclusion and any additional hypotheses are not reproduced in the supplied material. The conjecture is reported to be false, with an explicit 1010-vertex counterexample formally checked in Lean.

Sources & referencesView supporting material

Primary source

GitHub

Additional references

formal-mathematicsgraph-theory

Progress summary

Refreshed
Solved

A machine-checked ten-vertex counterexample settles the conjecture negatively, subject to the certificate’s stated trust assumptions.

The entry concerns WOWII Graph Conjecture 36; its full mathematical assertion is not reproduced in the scan. The latest report says the conjecture is false.

August 2026 machine-checked counterexample

An explicit ten-vertex counterexample was formally checked, with no reported $\mathrm{sorryAx}$. This settles the conjecture negatively in the formal system used, although the report does not establish peer review.

Current status (as of August 2026): The conjecture is settled false by a machine-checked ten-vertex counterexample; independent peer-reviewed confirmation remains absent.

Sources

Solutions 0

No solutions have been posted yet.