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The matrix tree theorem, also called Kirchhoff's matrix-tree theorem (Buekenhout and Parker 1998), states that the number of nonidentical spanning trees of a graph G is equal ...

A maximum spanning tree is a spanning tree of a weighted graph having maximum weight. It can be computed by negating the weights for each edge and applying Kruskal's ...

Polynomials m_k(x;beta,c) which form the Sheffer sequence for g(t) = ((1-c)/(1-ce^t))^beta (1) f(t) = (1-e^t)/(c^(-1)-e^t) (2) and have generating function ...

Let G be a graph with A and B two disjoint n-tuples of graph vertices. Then either G contains n pairwise disjoint AB-paths, each connecting a point of A and a point of B, or ...

An algorithm for finding roots which retains that prior estimate for which the function value has opposite sign from the function value at the current best estimate of the ...

An inequality which implies the correctness of the Robertson conjecture (Milin 1964). de Branges (1985) proved this conjecture, which led to the proof of the full Bieberbach ...

An edge coloring of a graph G is a coloring of the edges of G such that adjacent edges (or the edges bounding different regions) receive different colors. An edge coloring ...

A minimum edge cut of a graph is an edge cut of smallest possible size. The size of a minimum edge cut in a connected graph G is called the graph's edge connectivity ...

A minimum vertex cut of a graph is a vertex cut of smallest possible size. A vertex cut set of size 1 in a connected graph corresponds to an articulation vertex. The size of ...

Model theory is a general theory of interpretations of axiomatic set theory. It is the branch of logic studying mathematical structures by considering first-order sentences ...