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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 ...

There are a number of point processes which are called Hawkes processes and while many of these notions are similar, some are rather different. There are also different ...

A weakly binary tree is a planted tree in which all nonroot graph vertices are adjacent to at most three graph vertices. Let g(z)=sum_(i=0)^inftyg_iz^i, (1) be the generating ...

The Droz-Farny circles are a pair of circles of equal radius obtained by particular geometric constructions. The following amazing property of a triangle, first given by ...

The first Brocard point Omega is the interior point Omega (also denoted tau_1 or Z_1) of a triangle DeltaABC with points labeled in counterclockwise order for which the ...

Steiner gave and Droz-Farny (1901) proved that if equal circles are drawn about the vertices of a triangle (dashed circles in the above figure), they cut the lines joining ...

The second Brocard point is the interior point Omega^' (also denoted tau_2 or Z_2) of a triangle DeltaABC with points labeled in counterclockwise order for which the angles ...

Given triangle DeltaA_1A_2A_3, let the point of intersection of A_2Omega and A_3Omega^' be B_1, where Omega and Omega^' are the Brocard points, and similarly define B_2 and ...

Consider a reference triangle DeltaABC and externally inscribe a square on the side BC. Now join the new vertices S_(AB) and S_(AC) of this square with the vertex A, marking ...

A point is a 0-dimensional mathematical object which can be specified in n-dimensional space using an n-tuple (x_1, x_2, ..., x_n) consisting of n coordinates. In dimensions ...