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A single component algebraic link. Most knots up to 11 crossings are algebraic, but they quickly become outnumbered by nonalgebraic knots for more crossings (Hoste et al. ...

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

In general, it is possible to link two n-dimensional hyperspheres in (n+2)-dimensional space in an infinite number of inequivalent ways. In dimensions greater than n+2 in the ...

If a sequence of double points is passed as a closed curve is traversed, each double point appears once in an even place and once in an odd place.

The cycle double cover conjecture states that every bridgeless graph has a collection of cycles which together contain every edge exactly twice. This conjecture remains open, ...

Let all of the functions f_n(z)=sum_(k=0)^inftya_k^((n))(z-z_0)^k (1) with n=0, 1, 2, ..., be regular at least for |z-z_0|<r, and let F(z) = sum_(n=0)^(infty)f_n(z) (2) = (3) ...

A pair of prime numbers (p,q) such that p^(q-1)=1 (mod q^2) and q^(p-1)=1 (mod p^2). The only known examples are (2, 1093), (3, 1006003), (5 , 1645333507), (83, 4871), (911, ...

The Schläfli double sixes graph is the Levi graph of the double sixes configuration.

Let a knot K be n-embeddable. Then its tunnel number is a knot invariant which is related to n.

The clove hitch is the hitch illustrated above that is also called the boatman's knot or peg knot.