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Given a pick-7 lottery with 23 numbers that pays a prize to anyone matching at least 4 of the 7 numbers, there is a set of 253 tickets that guarantees a win. This set ...

A graphic sequence is a sequence of numbers which can be the degree sequence of some graph. A sequence can be checked to determine if it is graphic using GraphicQ[g] in the ...

A framework is called "just rigid" if it is rigid, but ceases to be so when any single bar is removed. Lamb (1928, pp. 93-94) proved that a necessary (but not sufficient) ...

A d-dimensional discrete percolation model on a regular point lattice L=L^d is said to be oriented if L is an oriented lattice. One common such model takes place on the ...

A snake is an Eulerian path in the d-hypercube that has no chords (i.e., any hypercube edge joining snake vertices is a snake edge). Klee (1970) asked for the maximum length ...

A circuit in which an entire graph is traversed in one route. Examples of curves that can be traced unicursally are the Mohammed sign and unicursal hexagram. The numbers of ...

If k|n, then the complete k-uniform hypergraph on n vertices decomposes into 1-factors, where a 1-factor is a set of n/k pairwise disjoint k-sets. Brouwer and Schrijver ...

An automorphism is an isomorphism of a system of objects onto itself. The term derives from the Greek prefix alphaupsilontauomicron (auto) "self" and ...

A bar graph is any plot of a set of data such that the number of data elements falling within one or more categories is indicated using a rectangle whose height or width is a ...

The diagonal of a polyhedron is any line segment connecting two nonadjacent vertices of the polyhedron. Any polyhedron having no diagonals must have a skeleton which is a ...