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The 600-cell is the finite regular four-dimensional polytope with Schläfli symbol {3,3,5}. It is also known as the hypericosahedron or hexacosichoron. It is composed of 600 ...

In general, the internal similitude center of two circles C_1=C(x_1,r_1) and C_2=C(x_2,r_2) with centers given in Cartesian coordinates is given by ...

A closed trail is called a circuit when it is specified in cyclic order but no first vertex is explicitly identified.

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).

The problem of deciding if four colors are sufficient to color any map on a plane or sphere.

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 ...

The braced square problem asks, given a hinged square composed of four equal rods (indicated by the red lines above), how many more hinged rods must be added in the same ...