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A fundamental structural result in extremal graph theory due to Szemerédi (1978). The regularity lemma essentially says that every graph can be well-approximated by the union ...

Every sufficiently large odd number is a sum of three primes (Vinogradov 1937). Ramachandra and Sankaranarayanan (1997) have shown that for sufficiently large n, the error ...

Let a random n×n (0,1)-matrix have entries which are 1 (with probability p) or 0 (with probability q=1-p) and numbers are assigned to the edges of a grid. A b-cluster is an ...

A class of knots containing the class of alternating knots. Let c(K) be the link crossing number. Then for knot sum K_1#K_2 which is an adequate knot, ...

In a graph G, two graph vertices are adjacent if they are joined by a graph edge.

Every finite-dimensional Lie algebra of characteristic p=0 has a faithful finite-dimensional representation.

An almost alternating link with a single component.

An almost unit is a nonunit in the integral domain of formal power series with a nonzero first coefficient, P=a_1x+a_2x^2+..., where a_1!=0. Under the operation of ...

A knot diagram which has alternating under- and overcrossings as the knot projection is traversed. The first knot which does not have an alternating diagram has 8 crossings.

Let K_1^n and K_2^n be disjoint bicollared knots in R^(n+1) or S^(n+1) and let U denote the open region between them. Then the closure of U is a closed annulus S^n×[0,1]. ...