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The Paris-Harrington theorem is a strengthening of the finite Ramsey's theorem by requiring that the homogeneous set be large enough so that cardH>=minH. Clearly, the ...

Partial derivatives are defined as derivatives of a function of multiple variables when all but the variable of interest are held fixed during the differentiation. (1) The ...

The (26,8)-Paulus graph having the largest possible graph automorphism group order of all 26-node Paulus graphs (namely 120) is sometimes known as the ...

There are at least 15 classes of convex pentagonal tilings, as illustrated above. The first five were discovered during investigations of German mathematician Karl Reinhardt ...

The pentagonal hexecontahedron is the 60-faced dual polyhedron of the snub dodecahedron A_8 (Holden 1971, p. 55). It is Wenninger dual W_(18). A tetrahedron 10-compound, cube ...

A perfect cuboid is a cuboid having integer side lengths, integer face diagonals d_(ab) = sqrt(a^2+b^2) (1) d_(ac) = sqrt(a^2+c^2) (2) d_(bc) = sqrt(b^2+c^2), (3) and an ...

Dirac (1952) proved that if the minimum vertex degree delta(G)>=n/2 for a graph G on n>=3 nodes, then G contains a Hamiltonian cycle (Bollobás 1978, Komlós et al. 1996). In ...

The numbers of positive definite n×n matrices of given types are summarized in the following table. For example, the three positive eigenvalues 2×2 (0,1)-matrices are [1 0; 0 ...

The probability density function (PDF) P(x) of a continuous distribution is defined as the derivative of the (cumulative) distribution function D(x), D^'(x) = ...

A quintic nonhamiltonian graph is a quintic graph that is nonhamiltonian. A number of such graphs are illustrated above. Owens (1980) showed that there exists a ...