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A counterexample to a conjecture of Graffiti.pc on the forest number

Contributed by Deep Bhattacharjee

Conjecture 66 of Graffiti.pc bounds the order of a largest induced forest of a connected graph from below by the even mode of the degrees of its complement divided by its average degree. We show that it is false, under every reading of its definitions and by an unbounded margin.

A mix of human-written and AI-generated textHuman understanding: some partsGraffiti.pccomplementcounterexampledegree sequenceforest numberinduced forest

Oct 23, 2026PDF ↗View work →

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A counterexample to a conjecture of Graffiti.pc on the forest number

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