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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2 Pith papers cite this work. Polarity classification is still indexing.
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math.CO 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Proves that graphs on N ≥ 2n vertices with δ(G) ≥ ⌊3N/4⌋ have every 2-edge-coloring containing a monochromatic copy of every n-vertex tree with max degree ≤ Δ.
citing papers explorer
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On Balance, To What Degree is Burr's Conjecture True?
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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A degree version of the Burr-Erd\H{o}s conjecture on trees
Proves that graphs on N ≥ 2n vertices with δ(G) ≥ ⌊3N/4⌋ have every 2-edge-coloring containing a monochromatic copy of every n-vertex tree with max degree ≤ Δ.