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Tutte (1971/72) conjectured that there are no 3-connected nonhamiltonian bicubic graphs. However, a counterexample was found by J. D. Horton in 1976 (Gropp 1990), and several ...

The Earth-Moon problem is a special case of the empire problem for countries with m=2 disjoint regions, with one region of each country lying on the Earth and one on the Moon ...

The Georges graph, illustrated above, is 50-node graph which is the smallest currently known example of a 3-connected bicubic nonhamiltonian graph. It is implemented in the ...

The midcircle of two given circles is the circle which would invert the circles into each other. Dixon (1991) gives constructions for the midcircle for four of the five ...

Rubik's Clock is a puzzle consisting of 18 small clocks, 14 of which are independent, each of which may be set to any 12-hour position. There are therefore 12^(14) possible ...

A number of areas of mathematics have the notion of a "dual" which can be applies to objects of that particular area. Whenever an object A has the property that it is equal ...

Draw an initial circle, and arrange six circles tangent to it such that they touch both the original circle and their two neighbors. Then the three lines joining opposite ...

A kit consisting of colored rods and slotted balls that can be used to construct three-dimensional configurations. The balls into which the rods are placed resemble an ...

Divide a triangle by its three medians into six smaller triangles. Surprisingly, the circumcenters O_(AB), O_(BA), etc. of the six circumcircles of these smaller triangles ...

A bicubic nonhamiltonian graph is a bicubic (i.e., bipartite cubic graph) that is nonhamiltonian (i.e., that does not possess a Hamiltonian cycle). Tutte (1971) conjectured ...