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A theory of Hamiltonian cycles.

A relation R on a set S is transitive provided that for all x, y and z in S such that xRy and yRz, we also have xRz.

Given a triangle, extend two sides in the direction opposite their common vertex. The circle tangent to these two lines and to the other side of the triangle is called an ...

If a points A^', B^', and C^' are marked on each side of a triangle DeltaABC, one on each side (or on a side's extension), then the three Miquel circles (each through a ...

A Ramsey number of the form R(k,k;2).

Edge splitting is the reverse of edge contraction.

An elegant algorithm for constructing an Eulerian cycle (Skiena 1990, p. 193).

As shown by Schur (1916), the Schur number S(n) satisfies S(n)<=R(n)-2 for n=1, 2, ..., where R(n) is a Ramsey number.

The Parts graphs are a set of unit-distance graphs with chromatic number five derived by Jaan Parts in 2019-2020 (Parts 2020a). They provide some of the smallest known ...

A topological space.