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- Cycle_basis abstract "In graph theory, a branch of mathematics, a cycle basis of an undirected graph is a set of simple cycles that forms a basis of the cycle space of the graph. That is, it is a minimal set of cycles that allows every Eulerian subgraph to be expressed as a symmetric difference of basis cycles.A fundamental cycle basis may be formed from any spanning tree or spanning forest of the given graph, by selecting the cycles that have exactly one edge that does not belong to the tree. Alternatively, if the edges of the graph have positive weights, the minimum weight cycle basis may be constructed in polynomial time.In planar graphs, the set of bounded cycles of an embedding of the graph forms a cycle basis. The minimum weight cycle basis of a planar graph corresponds to the Gomory–Hu tree of the dual graph.".
- Cycle_basis thumbnail Cycle_space_addition.svg?width=300.
- Cycle_basis wikiPageID "24778911".
- Cycle_basis wikiPageRevisionID "599746181".
- Cycle_basis subject Category:Algebraic_graph_theory.
- Cycle_basis comment "In graph theory, a branch of mathematics, a cycle basis of an undirected graph is a set of simple cycles that forms a basis of the cycle space of the graph. That is, it is a minimal set of cycles that allows every Eulerian subgraph to be expressed as a symmetric difference of basis cycles.A fundamental cycle basis may be formed from any spanning tree or spanning forest of the given graph, by selecting the cycles that have exactly one edge that does not belong to the tree.".
- Cycle_basis label "Cycle basis".
- Cycle_basis sameAs m.0_yhr7m.
- Cycle_basis sameAs Q16766188.
- Cycle_basis sameAs Q16766188.
- Cycle_basis wasDerivedFrom Cycle_basis?oldid=599746181.
- Cycle_basis depiction Cycle_space_addition.svg.
- Cycle_basis isPrimaryTopicOf Cycle_basis.
