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arXiv · 2608.15281

A Ten-Vertex Counterexample to a Conjecture on Unstable Graphs

Prateek R. Srivastava
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Abstract

Mizzi conjectured that every nontrivially unstable graph contains cycles C_k and C_{2k} for some odd k. We give a connected, nonbipartite, vertex-determining counterexample on ten vertices. Its instability is certified by an explicit nontrivial two-fold automorphism, and its complete set of simple-cycle lengths is {5,5,6}.

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Prateek R. Srivastava. 2026-08-15. A Ten-Vertex Counterexample to a Conjecture on Unstable Graphs. https://arxiv.org/abs/2608.15281

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