The spanning-tree spectrum of simple n-vertex graphs has cardinality at least exp(c n log n) for every fixed c < 1/4.
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math.CO 2years
2026 2verdicts
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Independent set counts for trees grow with exponent at least 0.1966; planar graphs achieve density one; graphs with linear edge density realize all positive integers via Zaremba's conjecture.
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The size of the spanning-tree spectrum of simple graphs
The spanning-tree spectrum of simple n-vertex graphs has cardinality at least exp(c n log n) for every fixed c < 1/4.
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Independent Sets and Continued Fractions
Independent set counts for trees grow with exponent at least 0.1966; planar graphs achieve density one; graphs with linear edge density realize all positive integers via Zaremba's conjecture.