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There are a number of meanings for the word "arc" in mathematics. In general, an arc is any smooth curve joining two points. The length of an arc is known as its arc length. ...

The phrase dependent percolation is used in two-dimensional discrete percolation to describe any general model in which the states of the various graph edges (in the case of ...

A domatic partition is a partition of the vertices of a graph into disjoint dominating sets. The maximum number of disjoint dominating sets in a domatic partition of a graph ...

The Floyd-Warshall algorithm, also variously known as Floyd's algorithm, the Roy-Floyd algorithm, the Roy-Warshall algorithm, or the WFI algorithm, is an algorithm for ...

A path in a graph G is a subgraph of G that is a path graph (West 2000, p. 20). The length of a path is the number of edges it contains. In most contexts, a path must contain ...

A formula satisfied by all Hamiltonian cycles with n nodes. Let f_j be the number of regions inside the circuit with j sides, and let g_j be the number of regions outside the ...

A cycle of a finite group G is a minimal set of elements {A^0,A^1,...,A^n} such that A^0=A^n=I, where I is the identity element. A diagram of a group showing every cycle in ...

A combinatorial conjecture formulated by Kneser (1955). It states that whenever the n-subsets of a (2n+k)-set are divided into k+1 classes, then two disjoint subsets end up ...

A lobster graph, lobster tree, or simply "lobster," is a tree having the property that the removal of leaf nodes leaves a caterpillar graph (Gallian 2007). The numbers of ...

Intuitively, a d-dimensional discrete percolation model is said to be long-range if direct flow is possible between pairs of graph vertices or graph edges which are "very ...