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A weakly connected digraph is a directed graph in which it is possible to reach any node starting from any other node by traversing edges in some direction (i.e., not ...

The blow-up lemma essentially says that regular pairs in Szemerédi's regularity lemma behave like complete bipartite graphs from the point of view of embedding bounded degree ...

There appears to be no standard term for a simple connected graph with exactly n edges, though the words "polynema" (Kyrmse) and "polyedge" (Muñiz 2011) have been proposed. ...

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 ...

The nullity of a linear transformation f:V->W of vector spaces is the dimension of its null space. The nullity and the map rank add up to the dimension of V, a result ...

A partition {a_1,...,a_n} is called graphical if there exists a graph G having degree sequence {a_1,...,a_n}. The number of graphical partitions of length n is equal to the ...

Let G=(V,E) be a finite graph, let Omega be the set Omega={0,1}^E whose members are vectors omega=(omega(e):e in E), and let F be the sigma-algebra of all subsets of Omega. A ...

Rubik's Clock is a puzzle consisting of 18 small clocks, 14 of which are independent, each of which may be set to any 12-hour position. There are therefore 12^(14) possible ...

A lattice polygon consisting of a closed self-avoiding walk on a square lattice. The perimeter, horizontal perimeter, vertical perimeter, and area are all well-defined for ...