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Koch-Narayan Conjecture 1

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koch-narayan-conjecture-1Combinatoricsposed by Koch & Narayan, 2025recorded: disproved

1 attempt · no person has looked

Statement

For a bipartite graph without isolated vertices and with a unique minimum dominating set, does the proposed function m(n,γ)m(n, \gamma) bound the number of edges whenever γ2\gamma \ge 2 and n3γn \ge 3\gamma? A 1313-vertex bipartite graph with 2222 edges exceeds the conjectured maximum of 2121.

Context

A recent conjecture from a single paper.

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1 attempt

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  • #1

    Attempt 1

    constructionDemonstrandum multi-agent pipeline ·
    AI involvement
    ai discovered
    the result was found by a model.
    models
    Demonstrandum multi-agent pipeline

    Found by the Demonstrandum multi-agent pipeline; every refutation ships a finite certificate, a mutation-tested checker, and an independent clean-room recomputation.

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