Combinatorics

The Lean Pool projects whose card's first MSC2020 code is in class 05, Combinatorics: 54 articles, one per card.

A proof of the Regts–Sevenster… to The Erdős–Sós conjecture (Erdős…

• A proof of the Regts–Sevenster conjecture, formalized
• Asymptotically attaining the Moore bound
• Balanced and vertex-distinguishing edge colourings
• BKLO simultaneous perfect matchings and spread matchings
• The Bollobás–Nikiforov conjecture
• Boolean Isoperimetry and Conway--Guy Coherent Gaps
• Brooks' theorem for subcubic graphs
• Chebyshev Quotients and Demazure Multiplicities
• Chip-Firing with Lean 4
• Chordal graphs: minimal separators and simplicial vertices
• Chvátal's conjecture and sharp Boolean correlation
• Classical graph colouring through lists, orientations and spectra
• Classical matching and factor theorems in finite graphs
• Clique trees, subtree representations and chordal treewidth
• Counterexamples to graph compactness and two-degenerate extremal bounds
• Counting Critical Portraits
• Demazure Operators and Lean
• The density Hales–Jewett theorem and Szemerédi's theorem
• Dross's fractional triangle decomposition theorem
• The Erdős–Sós conjecture (Erdős Problem 548)

Even graphs are edge-disjoint… to Near-perfect triangle packings…

• Even graphs are edge-disjoint unions of cycles
• Extended Demazure Product on ASP Permutations
• Finite hypergraph rounding and the asymptotic triangle-packing gap
• Finite max-flow / min-cut
• FrontierMath Ramsey Hypergraphs
• Fundamental groups of finite connected graphs
• Genus-Zero Pairings and Catalan Numbers
• Geometric Four-Colorings of the Moser Lattice and Ring
• Graph removal and extremal stability
• The Hajnal–Szemerédi theorem on equitable vertex colourings
• Hard-sphere Mayer NBC identity and fork-packing volume bound
• Häggkvist–Janssen list edge colouring of complete graphs
• Kahn–Kalai expectation-threshold theorem
• Known Bounds for the Hadwiger-Nelson Problem
• Kolokolnikov's ACMAX conjecture
• Line-graph colourings and matching decompositions
• Linear finite bipartization costs force countable graph colourings
• Maxima of Coxeter frieze patterns are Fibonacci numbers
• Nash-Williams–Tutte tree packing and arboricity
• Near-perfect triangle packings from sum-zero triples

Optimal Pebbling Number of the… to Vizing's theorem and equitable…

• Optimal Pebbling Number of the Hypercube
• Pólya's enumeration theorem
• Sabidussi's compatibility conjecture for Eulerian multigraphs
• The sharp finite-field Nikodym exponent
• Shelah's bound for the Hales–Jewett numbers
• The smallest critical set in a Latin square
• Split, cograph and threshold graph structures
• Strict Beck–Fiala rounding for incidence matrices
• Superexponential lower bounds for multicolor triangle Ramsey numbers
• The ten minimum universal collections of MacMahon cubes
• Turán's theorem (the "Book" weighting proof)
• Tutte’s path theorem for matroids
• Verified canonical labelling of finite graphs
• Vizing's theorem and equitable edge colourings

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