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The Loupekine snarks are the two snarks on 22 vertices and 33 edges illustrated above. They are implemented in the Wolfram Language as GraphData["LoupekineSnark1"] and ...

A matching, also called an independent edge set, on a graph G is a set of edges of G such that no two sets share a vertex in common. It is not possible for a matching on a ...

Martin Gardner (1975) played an April Fool's joke by asserting that the map of 110 regions illustrated above (left figure) required five colors and constitutes a ...

A vertex coloring is an assignment of labels or colors to each vertex of a graph such that no edge connects two identically colored vertices. A vertex coloring that minimize ...

The term multigraph refers to a graph in which multiple edges between nodes are either permitted (Harary 1994, p. 10; Gross and Yellen 1999, p. 4) or required (Skiena 1990, ...

If equilateral triangles DeltaABE_(AB), DeltaBCE_(BC), and DeltaACE_(AC) are erected externally on the sides of any triangle DeltaABC, then their centers N_(AB), N_(BC), and ...

The nearest integer function, also called nint or the round function, is defined such that nint(x) is the integer closest to x. While the notation |_x] is sometimes used to ...

Given an arrangement of points, a line containing just two of them is called an ordinary line. Dirac (1951) conjectured that every sufficiently set of n noncollinear points ...

An algorithm which can be used to find integer relations between real numbers x_1, ..., x_n such that a_1x_1+a_2x_2+...+a_nx_n=0, with not all a_i=0. Although the algorithm ...

A statement which appears self-contradictory or contrary to expectations, also known as an antinomy. Curry (1977, p. 5) uses the term pseudoparadox to describe an apparent ...