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The Steiner tree of some subset of the vertices of a graph G is a minimum-weight connected subgraph of G that includes all the vertices. It is always a tree. Steiner trees ...

The Ramsey number R(m,n) gives the solution to the party problem, which asks the minimum number of guests R(m,n) that must be invited so that at least m will know each other ...

The graph product denoted G-H and defined by the adjacency relations (gadjg^') or (g=g^' and hadjh^'). The graph lexicographic product is also known as the graph composition ...

Let I(G) denote the set of all independent sets of vertices of a graph G, and let I(G,u) denote the independent sets of G that contain the vertex u. A fractional coloring of ...

Two sets A and B are said to be independent if their intersection A intersection B=emptyset, where emptyset is the empty set. For example, {A,B,C} and {D,E} are independent, ...

A path constructed by repeatedly finding a path of positive capacity from a source to a sink and then adding it to the flow (Skiena 1990, p. 237). An augmenting path for a ...

A lattice L is said to be oriented if there exists a rule which assigns a specified direction to any edge connecting arbitrary lattice points x_i,x_j in L. In that way, an ...

The Q-chromatic polynomial, introduced by Birkhoff and Lewis (1946) and termed the "Q-chromial" by Bari (1974), is an alternate form of the chromatic polynomial pi(x) defined ...

A scale-free network is a connected graph or network with the property that the number of links k originating from a given node exhibits a power law distribution ...

A state diagram is a labeled directed graph together with state information that can be used to indicate that certain paths on in a system may be traversed only in a certain ...