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A problem asking for the shortest tour of a graph which visits each edge at least once (Kwan 1962; Skiena 1990, p. 194). For an Eulerian graph, an Eulerian cycle is the ...

R. C. Read defined the anarboricity of a graph G as the maximum number of edge-disjoint nonacyclic (i.e., cyclic) subgraphs of G whose union is G (Harary and Palmer 1973, p. ...

A maximal independent set is an independent set which is a maximal set, i.e., an independent set that is not a subset of any other independent set. The generic term "maximal ...

Let C^*(u) denote the number of nowhere-zero u-flows on a connected graph G with vertex count n, edge count m, and connected component count c. This quantity is called the ...

A Hamiltonian path, also called a Hamilton path, is a graph path between two vertices of a graph that visits each vertex exactly once. If a Hamiltonian path exists whose ...

A vertex-induced subgraph (sometimes simply called an "induced subgraph") is a subset of the vertices of a graph G together with any edges whose endpoints are both in this ...

A vertex cut, also called a vertex cut set or separating set (West 2000, p. 148), of a connected graph G is a subset of the vertex set S subset= V(G) such that G-S has more ...

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 ...

"Neighborhood" is a word with many different levels of meaning in mathematics. One of the most general concepts of a neighborhood of a point x in R^n (also called an ...

The chromatic number of a graph G is the smallest number of colors needed to color the vertices of G so that no two adjacent vertices share the same color (Skiena 1990, p. ...