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A Jordan curve is a plane curve which is topologically equivalent to (a homeomorphic image of) the unit circle, i.e., it is simple and closed. It is not known if every Jordan ...

It is possible to find six points in the plane, no three on a line and no four on a circle (i.e., none of which are collinear or concyclic), such that all the mutual ...

A graph is called cordial if it is possible to label its vertices with 0s and 1s so that when the edges are labeled with the difference of the labels at their endpoints, the ...

The empire problem, also known as the m-pire problem) asks for the maximum number of colors needed to color countries such that no two countries sharing a common border have ...

A cubic map is three-colorable iff each interior region is bounded by an even number of regions. A non-cubic map bounded by an even number of regions is not necessarily ...

A topological space in which every point has a countable neighborhood system base for its neighborhood system.

An integral which has neither limit infinite and from which the integrand does not approach infinity at any point in the range of integration.

The tangential triangle is the triangle DeltaT_AT_BT_C formed by the lines tangent to the circumcircle of a given triangle DeltaABC at its vertices. It is therefore antipedal ...

A graceful permutation sigma on n letters is a permutation such that {|sigma(i)-sigma(i+1)|:i=1,2,...,n-1}={1,2,...,n-1}. For example, there are four graceful permutations on ...

Another word for a C^infty (infinitely differentiable) manifold, also called a differentiable manifold. A smooth manifold is a topological manifold together with its ...