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An s-route of a graph G is a sequence of vertices (v_0,v_1,...,v_s) of G such that v_iv_(i+1) in E(G) for i=0, 1, ..., s-1 (where E(G) is the edge set of G) and ...

Suppose a line L^' meets sidelines BC, CA, and AB in points A^', B^', and C^', respectively. Let A^('') be the reflection of A^' about the midpoint of segment BC, and ...

A generalization of Ramsey theory to mathematical objects in which one would not normally expect structure to be found. For example, there exists a graph with very few ...

Every semisimple Lie algebra g is classified by its Dynkin diagram. A Dynkin diagram is a graph with a few different kinds of possible edges. The connected components of the ...

A curve in two dimensions on which the value of a function f(x,y) is a constant. Other synonymous terms are isarithm, isopleth, and contour line. A plot of several ...

The circles on the polygon diagonals of a complete quadrilateral as diameters are coaxal. Furthermore, the orthocenters of the four triangles of a complete quadrilateral are ...

The real axis is the line in the complex plane corresponding to zero imaginary part, I[z]=0. Every real number corresponds to a unique point on the real axis.

A Woo circle is an Archimedean circle with center on the Schoch line and tangent to certain other circles. An applet for investigating Woo circles and Schoch lines has been ...

A member of a collection of sets is said to be maximal if it cannot be expanded to another member by addition of any element. Maximal sets are important in graph theory since ...

Given a collection of sets, a member set that is not a proper subset of another member set is called a minimal set. Minimal sets are important in graph theory, since many ...