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The maximum number of disjoint dominating sets in a domatic partition of a graph G is called its domatic number d(G). The domatic number should not be confused with the ...

A principal vertex x_i of a simple polygon P is called an ear if the diagonal [x_(i-1),x_(i+1)] that bridges x_i lies entirely in P. Two ears x_i and x_j are said to overlap ...

An edge cover is a subset of edges defined similarly to the vertex cover (Skiena 1990, p. 219), namely a collection of graph edges such that the union of edge endpoints ...

The size of a minimum edge cover in a graph G is known as the edge cover number of G, denoted rho(G). If a graph G has no isolated points, then nu(G)+rho(G)=|G|, where nu(G) ...

A family of functors H_n(·) from the category of pairs of topological spaces and continuous maps, to the category of Abelian groups and group homomorphisms satisfies the ...

Is there a planar convex set having two distinct equichordal points? The problem was first proposed by Fujiwara (1916) and Blaschke et al. (1917), but long defied solution. ...

Euclidean n-space, sometimes called Cartesian space or simply n-space, is the space of all n-tuples of real numbers, (x_1, x_2, ..., x_n). Such n-tuples are sometimes called ...

1. A straight line segment can be drawn joining any two points. 2. Any straight line segment can be extended indefinitely in a straight line. 3. Given any straight line ...

The four parameters e_0, e_1, e_2, and e_3 describing a finite rotation about an arbitrary axis. The Euler parameters are defined by e_0 = cos(phi/2) (1) e = [e_1; e_2; e_3] ...

Given triangle DeltaABC, there are four lines simultaneously tangent to the B- and C-excircles (with centers J_B and J_C, respectively). Of these, three correspond to the ...