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Let S be a collection of subsets of a finite set X. A subset Y of X that meets every member of S is called the vertex cover, or hitting set. A vertex cover of a graph G can ...

A regular graph that is not strongly regular is known as a weakly regular graph. There are no weakly regular simple graphs on fewer than six nodes, and the numbers on n=6, 7, ...

The Wigner 6j-symbols (Messiah 1962, p. 1062), commonly simply called the 6j-symbols, are a generalization of Clebsch-Gordan coefficients and Wigner 3j-symbol that arise in ...

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 ...

A problem posed by the Slovak mathematician Stefan Znám in 1972 asking whether, for all integers k>=2, there exist k integers x_1,...,x_k all greater than 1 such that x_i is ...

As a consequence of Matiyasevich's refutation of Hilbert's 10th problem, it can be proved that there does not exist a general algorithm for solving a general quartic ...

The prime number theorem gives an asymptotic form for the prime counting function pi(n), which counts the number of primes less than some integer n. Legendre (1808) suggested ...

A Mersenne prime is a Mersenne number, i.e., a number of the form M_n=2^n-1, that is prime. In order for M_n to be prime, n must itself be prime. This is true since for ...

Let p be a prime with n digits and let A be a constant. Call p an "A-prime" if the concatenation of the first n digits of A (ignoring the decimal point if one is present) ...

The hundred-dollar, hundred-digits challenge problems are a set of ten problems in numerical analysis published in the January/February 2002 issue of SIAM News ...