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· 2002 · DOI 10.1007/s004930200014

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On Balance, To What Degree is Burr's Conjecture True?

math.CO · 2026-06-09 · unverdicted · novelty 7.0

For lopsided trees with t2 >= 2 t1, Burr's bound has a gap of order max(t1^2/t2, sqrt(t1)); for t2 >= 500 t1 the bound is tight if Delta(T) <= t2 - t1 but off by Omega(log t2) otherwise.

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  • On Balance, To What Degree is Burr's Conjecture True? math.CO · 2026-06-09 · unverdicted · none · ref 8

    For lopsided trees with t2 >= 2 t1, Burr's bound has a gap of order max(t1^2/t2, sqrt(t1)); for t2 >= 500 t1 the bound is tight if Delta(T) <= t2 - t1 but off by Omega(log t2) otherwise.