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Zarankiewicz's conjecture asserts that graph crossing number for a complete bipartite graph K_(m,n) is Z(m,n)=|_n/2_||_(n-1)/2_||_m/2_||_(m-1)/2_|, (1) where |_x_| is the ...

The term "transition matrix" is used in a number of different contexts in mathematics. In linear algebra, it is sometimes used to mean a change of coordinates matrix. In the ...

One of the numbers ..., -2, -1, 0, 1, 2, .... The set of integers forms a ring that is denoted Z. A given integer n may be negative (n in Z^-), nonnegative (n in Z^*), zero ...

The square-triangle theorem states that any nonnegative integer can be represented as the sum of a square, an even square, and a triangular number (Sun 2005), i.e., ...

Vizing's theorem states that a graph can be edge-colored in either Delta or Delta+1 colors, where Delta is the maximum vertex degree of the graph. A graph with edge chromatic ...

Let s_1, s_2, ... be an infinite series of real numbers lying between 0 and 1. Then corresponding to any arbitrarily large K, there exists a positive integer n and two ...

Minkowski's question mark function is the function y=?(x) defined by Minkowski for the purpose of mapping the quadratic surds in the open interval (0,1) into the rational ...

A labeling phi of (the vertices) of a graph G with positive integers taken from the set {1,2,...,r} is said to be r-distinguishing if no graph automorphism of G preserves all ...

A doublecross graph is a graph with graph crossing number 2. The numbers of doublecross simple graphs on n=1 nodes are 0, 0, 0, 0, 0, 1, 39, ..., and the numbers of connected ...

A theorem due to Conway et al. (1997) which states that, if a positive definite quadratic form with integer matrix entries represents all natural numbers up to 15, then it ...