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If M^3 is a closed oriented connected 3-manifold such that every simple closed curve in M lies interior to a ball in M, then M is homeomorphic with the hypersphere, S^3.

A search algorithm of a graph which explores all nodes adjacent to the current node before moving on. For cyclic graphs, care must be taken to make sure that no nodes are ...

Grünbaum conjectured that for every m>1, n>2, there exists an m-regular, m-chromatic graph of girth at least n. This result is trivial for n=2 or m=2,3, but only a small ...

Given a point lattice, a cluster is a group of filled cells which are all connected to their neighbors vertically or horizontally.

Complete digraphs are digraphs in which every pair of nodes is connected by a bidirectional edge.

An n-component of a graph G is a maximal n-connected subgraph.

The cotree T^* of a spanning tree T in a connected graph G is the spacing subgraph of G containing exactly those edges of G which are not in T (Harary 1994, p. 39).

Cubic graphs, also called trivalent graphs, are graphs all of whose nodes have degree 3 (i.e., 3-regular graphs). Cubic graphs on n nodes exists only for even n (Harary 1994, ...

A rewriting of a given quantity (e.g., a matrix) in terms of a combination of "simpler" quantities.

The disorder number of a simple connected graph on n vertices is defined as the maximum length of a walk along the edges of the graph taken over all ordering of its vertices ...