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The bandwidth of a matrix M=(m_(ij)) is the maximum value of |i-j| such that m_(ij) is nonzero.

A tree spread in which each node has a finite number of children.

A theory of Hamiltonian cycles.

A relation R on a set S is transitive provided that for all x, y and z in S such that xRy and yRz, we also have xRz.

A closed trail is called a circuit when it is specified in cyclic order but no first vertex is explicitly identified.

A Ramsey number of the form R(k,k;2).

An elegant algorithm for constructing an Eulerian cycle (Skiena 1990, p. 193).

The problem of deciding if four colors are sufficient to color any map on a plane or sphere.

As shown by Schur (1916), the Schur number S(n) satisfies S(n)<=R(n)-2 for n=1, 2, ..., where R(n) is a Ramsey number.

The braced square problem asks, given a hinged square composed of four equal rods (indicated by the red lines above), how many more hinged rods must be added in the same ...