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Fractional Matching
In graph theory, a fractional matching is a generalization of a matching in which, intuitively, each vertex may be broken into fractions that are matched to different neighbor vertices. Definition Given a graph G=(V,E), a fractional matching in G is a function that assigns, to each edge e\in E, a fraction f(e)\in ,1/math>, such that for every vertex v\in V, the sum of fractions of edges adjacent to v is at most one: \forall v\in V: \sum_f(e)\leq 1 A matching in the traditional sense is a special case of a fractional matching, in which the fraction of every edge is either zero or one: f(e)=1 if e is in the matching, and f(e)=0 if it is not. For this reason, in the context of fractional matchings, usual matchings are sometimes called ''integral matchings''. Size The size of an integral matching is the number of edges in the matching, and the matching number \nu(G) of a graph G is the largest size of a matching in G. Analogously, the ''size'' of a fractional matching is the sum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Theory
In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph theory), vertices'' (also called ''nodes'' or ''points'') which are connected by ''Glossary of graph theory terms#edge, edges'' (also called ''arcs'', ''links'' or ''lines''). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics. Definitions Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures. Graph In one restricted but very common sense of the term, a graph is an ordered pair G=(V,E) comprising: * V, a Set (mathematics), set of vertices (also called nodes or points); * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
