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Vizing's theorem states that a graph can be edge-colored in either Delta or Delta+1 colors, where Delta is the maximum vertex degree of the graph. A graph with edge chromatic ...

Each of the sacred unit fractions which the ancient Egyptians attributed to the six parts of the eye of the god Horus: 1/2, 1/4, 1/8, 1/16, 1/32, and 1/64. These fractions, ...

Let G be an undirected graph, and let i denote the cardinal number of the set of externally active edges of a spanning tree T of G, j denote the cardinal number of the set of ...

Let Pi be a permutation of n elements, and let alpha_i be the number of permutation cycles of length i in this permutation. Picking Pi at random, it turns out that ...

A k-matching in a graph G is a set of k edges, no two of which have a vertex in common (i.e., an independent edge set of size k). Let Phi_k be the number of k-matchings in ...

The Mephisto waltz sequence is defined by beginning with 0 and then iterating the maps 0->001 and 1->110. This gives 0, 001, 001001110, 001001110001001110110110001, ... (OEIS ...

A mathematical object defined for a set and a binary operator in which the multiplication operation is associative. No other restrictions are placed on a semigroup; thus a ...

A discriminant is a quantity (usually invariant under certain classes of transformations) which characterizes certain properties of a quantity's roots. The concept of the ...

A set of algebraic invariants for a quantic such that any invariant of the quantic is expressible as a polynomial in members of the set. Gordan (1868) proved the existence of ...

A monoid is a set that is closed under an associative binary operation and has an identity element I in S such that for all a in S, Ia=aI=a. Note that unlike a group, its ...