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The fraction eta of a volume filled by a given collection of solids.

A graph G is called d-polytopal if there exists a d-dimensional convex polytope P such that the vertices and edges of G are in a one-to-one incidence-preserving ...

A planar graph corresponding to polyhedra skeletons. The polyhedral graphs are special cases.

A shuffle-exchange graph is a nonsimple graph (due to the existence of graph loops) whose vertices are length n binary strings with an edge from w to w^' if 1. w^' differs ...

The small world problem asks for the probability that two people picked at random have at least one acquaintance in common.

Maximize the amount of floor space which can be covered with a fixed tile (Hoffman 1998, p. 173).

A graph G is transitive if any three vertices (x,y,z) such that edges (x,y),(y,z) in G imply (x,z) in G. Unlabeled transitive digraphs are called digraph topologies.

The 3-node tournament (and directed graph) illustrated above (Harary 1994, p. 205).

A weakly connected component of a simple directed graph (i.e., a digraph without loops) is a maximal subdigraph such that for every pair of distinct vertices u, v in the ...

A box can be packed with a harmonic brick a×ab×abc iff the box has dimensions ap×abq×abcr for some natural numbers p, q, r (i.e., the box is a multiple of the brick).