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The maximum flow between vertices v_i and v_j in a graph G is exactly the weight of the smallest set of edges to disconnect G with v_i and v_j in different components (Ford ...

Suppose that G is a pseudograph, E is the edge set of G, and C is the family of edge sets of graph cycles of G. Then C obeys the axioms for the circuits of a matroid, and ...

A vector field X on a compact foliated manifold (M,F) is nice if X is transverse to F and if X has a closed orbit C (called a nice orbit) such that the intersection C ...

A rational number is a number that can be expressed as a fraction p/q where p and q are integers and q!=0. A rational number p/q is said to have numerator p and denominator ...

A group G is a finite or infinite set of elements together with a binary operation (called the group operation) that together satisfy the four fundamental properties of ...

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 of ...

The constants lambda_(m,n)=inf_(r in R_(m,n))sup_(x>=0)|e^(-x)-r(x)|, where r(x)=(p(x))/(q(x)), p and q are mth and nth order polynomials, and R_(m,n) is the set of all ...

Every "large" even number may be written as 2n=p+m where p is a prime and m in P union P_2 is the set of primes P and semiprimes P_2.

A level set in two dimensions. Phase curves are sometimes also known as level curves (Tabor 1989, p. 14).

Any set of n+2 points in R^n can always be partitioned in two subsets V_1 and V_2 such that the convex hulls of V_1 and V_2 intersect.