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Any complete graph is a core. A cycle of odd length is a core. A graph is a core if and only if the core of is equal to . Every two cycles of even length, and more generally every two bipartite graphs are hom-equivalent. The core of each of these graphs is the two-vertex complete graph K 2.
A graph is k-choosable (or k-list-colorable) if it has a proper list coloring no matter how one assigns a list of k colors to each vertex. The choosability (or list colorability or list chromatic number) ch(G) of a graph G is the least number k such that G is k-choosable. More generally, for a function f assigning a positive integer f(v) to ...
In graph theory, a k-degenerate graph is an undirected graph in which every subgraph has at least one vertex of degree at most k: that is, some vertex in the subgraph touches k or fewer of the subgraph's edges. The degeneracy of a graph is the smallest value of k for which it is k-degenerate.
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A claw is a tree with one internal vertex and three leaves, or equivalently the complete bipartite graph K 1,3. A claw-free graph is a graph that does not have an induced subgraph that is a claw. clique A clique is a set of mutually adjacent vertices (or the complete subgraph induced by that set). Sometimes a clique is defined as a maximal set ...
The following sections cover the way of presenting simple inline formulae in HTML, instead of using LaTeX. Templates supporting HTML formatting are listed in Category:Mathematical formatting templates. Not all templates are recommended for use; in particular, use of the {} template to format fractions is discouraged in mathematics articles.
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A complete graph with n nodes represents the edges of an (n – 1)-simplex. Geometrically K 3 forms the edge set of a triangle, K 4 a tetrahedron, etc. The Császár polyhedron, a nonconvex polyhedron with the topology of a torus, has the complete graph K 7 as its skeleton. [15] Every neighborly polytope in four or more dimensions also has a ...