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A graphic sequence is a sequence of numbers which can be the degree sequence of some graph. A sequence can be checked to determine if it is graphic using GraphicQ[g] in the ...

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 circuit in which an entire graph is traversed in one route. Examples of curves that can be traced unicursally are the Mohammed sign and unicursal hexagram. The numbers of ...

A weak snark is a cyclically 4-edge connected cubic graph with edge chromatic number 4 and girth at least 4 (Brinkmann et al. 2013). Weak snarks therefore represent a more ...

The Icosian game, also called the Hamiltonian game (Ball and Coxeter 1987, p. 262), is the problem of finding a Hamiltonian cycle along the edges of an dodecahedron, i.e., a ...

The score sequence of a tournament is a monotonic nondecreasing sequence of the outdegrees of the graph vertices of the corresponding tournament graph. Elements of a score ...

The traveling salesman problem is a problem in graph theory requiring the most efficient (i.e., least total distance) Hamiltonian cycle a salesman can take through each of n ...

A labeled binary tree containing the labels 1 to n with root 1, branches leading to nodes labeled 2 and 3, branches from these leading to 4, 5 and 6, 7, respectively, and so ...

A labeled ternary tree containing the labels 1 to n with root 1, branches leading to nodes labeled 2, 3, 4, branches from these leading to 5, 6, 7 and 8, 9, 10 respectively, ...

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 ...