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If the top and bottom bases of a solid are equal in area, lie in parallel planes, and every section of the solid parallel to the bases is equal in area to that of the base, ...

In the calculus of variations, the condition f_(y^')(x,y,y^'(x_-))=f_(y^')(x,y,y^'(x_+)) must hold at a corner (x,y) of a minimizing arc E_(12).

If there is a (nu,nu^') correspondence between two curves of curve genus p and p^' and the number of branch points properly counted are beta and beta^', then ...

Algebra

A k-factor of a graph is a k-regular subgraph of order n. k-factors are a generalization of complete matchings. A perfect matching is a 1-factor (Skiena 1990, p. 244).

A graph G is k-factorable if it is the union of disjoint k-factors (Skiena 1990, p. 244).

A clique of a graph G is a complete subgraph of G, and the clique of largest possible size is referred to as a maximum clique (which has size known as the (upper) clique ...

The join G=G_1+G_2 of graphs G_1 and G_2 with disjoint point sets V_1 and V_2 and edge sets X_1 and X_2 is the graph union G_1 union G_2 together with all the edges joining ...

The Johnson solids are the convex polyhedra having regular faces and equal edge lengths (with the exception of the completely regular Platonic solids, the "semiregular" ...

The term "(a,b)-leaper" (sometimes explicitly called a "single-pattern leaper") describes a fairy chess piece such as a knight that may make moves which simultaneously change ...