A quantitative ergodic theory proof of Szemerédi's theorem.
A quantum field theoretical representation of Euler-Zagier sums.
A quasi-spectral characterization of strongly distance-regular graphs.
A quasisymmetric function generalization of the chromatic symmetric function.
A rainbow -matching in the complete graph with colors.
A Ramsey treatment of symmetry.
A Ramsey-style extension of a theorem of Erdős and Hajnal
If n, t are natural numbers, μ is an infinite cardinal, G is an n-chromatic graph of cardinality at most μ, then there is a graph X with , |X| = μ⁺, such that every subgraph of X of cardinality < t is n-colorable.
A Ramsey-Type Problem for Paths in Digraphs.
A ramsey-type theorem for multiple disjoint copies of induced subgraphs
Let k and ℓ be positive integers with ℓ ≤ k − 2. It is proved that there exists a positive integer c depending on k and ℓ such that every graph of order (2k−1−ℓ/k)n+c contains n vertex disjoint induced subgraphs, where these subgraphs are isomorphic to each other and they are isomorphic to one of four graphs: (1) a clique of order k, (2) an independent set of order k, (3) the join of a clique of order ℓ and an independent set of order k − ℓ, or (4) the union of an independent set of order ℓ and...
A random graph model for power law graphs.
A random walk on the rook placements on a Ferrers board.
A reciprocity theorem for domino tilings.
A recurrence relation for the “inv" analogue of -Eulerian polynomials.
A Recursive Construction for Room Designs
A recursive construction of 1-rotational Steiner 2-designs.
A recursive construction of asymmetric 1-factorisations.
A recursive relation for weighted Motzkin sequences.
A Reduction of Lattice Tiling by Translates of a Cubical Cluster.
A Reduction of the Graph Reconstruction Conjecture
A graph is said to be reconstructible if it is determined up to isomor- phism from the collection of all its one-vertex deleted unlabeled subgraphs. Reconstruction Conjecture (RC) asserts that all graphs on at least three vertices are reconstructible. In this paper, we prove that interval-regular graphs and some new classes of graphs are reconstructible and show that RC is true if and only if all non-geodetic and non-interval-regular blocks G with diam(G) = 2 or diam(Ḡ) = diam(G) = 3 are reconstructible...
A refinement of a partition theorem of Sellers.