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A space X is locally pathwise-connected if for every neighborhood around every point in X, there is a smaller, pathwise-connected neighborhood.

The connected domination number of a connected graph G, denoted d(G), is the size of a minimum connected dominating set of a graph G. The maximum leaf number l(G) and ...

The expression im kleinen is German and means "on a small scale." A topological space is connected im kleinen at a point x if every neighborhood U of x contains an open ...

A topological space X is semilocally simply connected (also called semilocally 1-connected) if every point x in X has a neighborhood U such that any loop L:[0,1]->U with ...

A maximal subgraph of an undirected graph such that any two edges in the subgraph lie on a common simple cycle.

Every compact 3-manifold is the connected sum of a unique collection of prime 3-manifolds.

A graph is k-edge-connected if there does not exist a set of k-1 edges whose removal disconnects the graph (Skiena 1990, p. 177). The maximum edge connectivity of a given ...

A hyperstring is a simple semi-Hamiltonian acyclic digraph (V,E) with a labeling of the edges in E such that, for all vertices i,j,p,q in V, either pi(i,j)=pi(p,q) or pi(i,j) ...

A square n×n matrix A=a_(ij) is called reducible if the indices 1, 2, ..., n can be divided into two disjoint nonempty sets i_1, i_2, ..., i_mu and j_1, j_2, ..., j_nu (with ...

The 12-vertex graph consisting of a cube in which two opposite faces (say, top and bottom) have edges drawn across them which connect the centers of opposite sides of the ...