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For an integer n>=2, let lpf(n) denote the least prime factor of n. A pair of integers (x,y) is called a twin peak if 1. x<y, 2. lpf(x)=lpf(y), 3. For all z, x<z<y implies ...

A number of strongly regular graphs of several types derived from combinatorial design were identified by Goethals and Seidel (1970). Theorem 2.4 of Goethals and Seidel ...

The Celmins-Swart snarks are the two snarks on 26 vertices and 39 edges illustrated above. They are implemented in the Wolfram Language as GraphData["CelminsSwartSnark1"] and ...

A fusene is a simple planar 2-connected graph embedded in the plane with all vertices of degree 2 or 3, all bounded faces (not necessarily regular) hexagons, and all vertices ...

The first (called the "Blanuša double" by Orbanić et al. 2004) and second (called the "Blanuša snark" by Orbanić et al. 2004) Blanuša snarks were the second and third snarks ...

A snark on 30 vertices with edge chromatic number 4. It is implemented in the Wolfram Language as GraphData["DoubleStarSnark"].

A matching is a maximum matching iff it contains no augmenting path.

The term "square" can be used to mean either a square number ("x^2 is the square of x") or a geometric figure consisting of a convex quadrilateral with sides of equal length ...

The Watkins snark is the snark on 50 vertices ad 75 nodes illustrated above. It is implemented in the Wolfram Language as GraphData["WatkinsSnark"].

A fork of a tree T is a node of T which is the endpoint of two or more branches.