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The Fritsch graph is the 9-node planar graph illustrated above that tangles the Kempe chains in Kempe's algorithm and thus provides an example of how Kempe's supposed proof ...

A helix, sometimes also called a coil, is a curve for which the tangent makes a constant angle with a fixed line. The shortest path between two points on a cylinder (one not ...

Let s_k be the number of independent vertex sets of cardinality k in a graph G. The polynomial I(x)=sum_(k=0)^(alpha(G))s_kx^k, (1) where alpha(G) is the independence number, ...

LCF notation is a concise and convenient notation devised by Joshua Lederberg (winner of the 1958 Nobel Prize in Physiology and Medicine) for the representation of cubic ...

Percolation, the fundamental notion at the heart of percolation theory, is a difficult idea to define precisely though it is quite easy to describe qualitatively. From the ...

An analog of the polyominoes and polyiamonds in which collections of regular hexagons are arranged with adjacent sides. They are also called hexes, hexas, or polyfrobs ...

A random-connection model (RCM) is a graph-theoretic model of continuum percolation theory characterized by the existence of a stationary point process X and a non-increasing ...

A prime p is said to be a Sophie Germain prime if both p and 2p+1 are prime. The first few Sophie Germain primes are 2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, 131, ... (OEIS ...

A superellipse is a curve with Cartesian equation |x/a|^r+|y/b|^r=1, (1) first discussed in 1818 by Lamé. A superellipse may be described parametrically by x = acos^(2/r)t ...

Tait's Hamiltonian graph conjecture asserted that every cubic polyhedral graph is Hamiltonian. It was proposed by Tait in 1880 and refuted by Tutte (1946) with a ...