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The Nechushtan graph, illustrated above, is a 10-vertex 5-chromatic graph that is unit-distance in 3 dimensions. It was used by Nechushtan (2002) in the construction of of a ...

A number of graphs are associated with P. J. Owens. The 76-node Owens graph (Owens 1980) provides the smallest known example of a polyhedral quintic nonhamiltonian graph. It ...

The graph complement of a perfect graph is itself perfect. Originally known as the weak perfect graph conjecture (Fulkerson 1971), the result was subsequently proved by ...

A simple polyhedron, also called a simplicial polyhedron, is a polyhedron that is topologically equivalent to a sphere (i.e., if it were inflated, it would produce a sphere) ...

To color any map on the sphere or the plane requires at most six-colors. This number can easily be reduced to five, and the four-color theorem demonstrates that the necessary ...

X is a spherical t-design in E iff it is possible to exactly determine the average value on E of any polynomial f of degree at most t by sampling f at the points of X. In ...

There are a number of interesting results related to the tiling of squares. For example, M. Laczkovich has shown that there are exactly three shapes of non-right triangles ...

Given a circular table of diameter 9 feet, which is the minimal number of planks (each 1 foot wide and length greater than 9 feet) needed in order to completely cover the ...

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 convex polyhedron is defined as the set of solutions to a system of linear inequalities mx<=b (i.e., a matrix inequality), where m is a real s×d matrix and b is a real ...