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Voronin (1975) proved the remarkable analytical property of the Riemann zeta function zeta(s) that, roughly speaking, any nonvanishing analytic function can be approximated ...

A minimum vertex cover is a vertex cover having the smallest possible number of vertices for a given graph. The size of a minimum vertex cover of a graph G is known as the ...

The operator I^~ which takes a real number to the same real number I^~r=r.

Let S be a nonempty set of real numbers that has a lower bound. A number c is the called the greatest lower bound (or the infimum, denoted infS) for S iff it satisfies the ...

Let S be a nonempty set of real numbers that has an upper bound. Then a number c is called the least upper bound (or the supremum, denoted supS) for S iff it satisfies the ...

A pair of vertices (x,y) of a graph G is called an omega-critical pair if omega(G+xy)>omega(G), where G+xy denotes the graph obtained by adding the edge xy to G and omega(H) ...

A definition assigns properties to some sort of mathematical object. For example, Euclid's Elements starts with a number of definitions, such as "a line is a breadthless ...

Two nonisomorphic graphs are said to be chromatically equivalent (also termed "chromically equivalent by Bari 1974) if they have identical chromatic polynomials. A graph that ...

The term "loop" has a number of meanings in mathematics. Most simply, a loop is a closed curve whose initial and final points coincide in a fixed point p known as the ...

The circle H which touches the incircles I, I_A, I_B, and I_C of a circular triangle ABC and its associated triangles. It is either externally tangent to I and internally ...