Establishes the first exponential improvement since 1947 to the lower bound on off-diagonal Ramsey numbers r(ℓ, Cℓ) for constant C > 1.
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5 Pith papers cite this work, alongside 2 external citations. Polarity classification is still indexing.
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UNVERDICTED 5representative citing papers
This work charts a nuanced complexity landscape for diameter computation on 2D intersection graphs, delivering new subquadratic algorithms for some object types and diameter values while proving hardness for others under fine-grained assumptions.
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.
Multicolour Ramsey numbers for many copies of H are determined up to additive (or linear) error via (H,r)-gadgets, with random analogues generalising Rödl–Ruciński.
Simplified proof of exponential Ramsey lower bound improvements via Gaussian random graphs, with better quantitative constants than prior work.
citing papers explorer
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An exponential improvement for Ramsey lower bounds
Establishes the first exponential improvement since 1947 to the lower bound on off-diagonal Ramsey numbers r(ℓ, Cℓ) for constant C > 1.
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Charting the Diameter Computation Landscape on Intersection Graphs in the Plane
This work charts a nuanced complexity landscape for diameter computation on 2D intersection graphs, delivering new subquadratic algorithms for some object types and diameter values while proving hardness for others under fine-grained assumptions.
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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.
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Ramsey numbers of multiple copies of a graph and the random Ramsey theorem
Multicolour Ramsey numbers for many copies of H are determined up to additive (or linear) error via (H,r)-gadgets, with random analogues generalising Rödl–Ruciński.
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Gaussian random graphs and Ramsey numbers
Simplified proof of exponential Ramsey lower bound improvements via Gaussian random graphs, with better quantitative constants than prior work.