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- Minimum_spanning_tree abstract "Given a connected, undirected graph, a spanning tree of that graph is a subgraph that is a tree and connects all the vertices together. A single graph can have many different spanning trees. We can also assign a weight to each edge, which is a number representing how unfavorable it is, and use this to assign a weight to a spanning tree by computing the sum of the weights of the edges in that spanning tree. A minimum spanning tree (MST) or minimum weight spanning tree is then a spanning tree with weight less than or equal to the weight of every other spanning tree. More generally, any undirected graph (not necessarily connected) has a minimum spanning forest, which is a union of minimum spanning trees for its connected components.One example would be a telecommunications company laying cable to a new neighborhood. If it is constrained to bury the cable only along certain paths, then there would be a graph representing which points are connected by those paths. Some of those paths might be more expensive, because they are longer, or require the cable to be buried deeper; these paths would be represented by edges with larger weights. A spanning tree for that graph would be a subset of those paths that has no cycles but still connects to every house. There might be several spanning trees possible. A minimum spanning tree would be one with the lowest total cost.".
- Minimum_spanning_tree thumbnail Minimum_spanning_tree.svg?width=300.
- Minimum_spanning_tree wikiPageExternalLink nesetril00otakar.html.
- Minimum_spanning_tree wikiPageExternalLink 12-mst.pdf.
- Minimum_spanning_tree wikiPageExternalLink table_of_contents.html.
- Minimum_spanning_tree wikiPageExternalLink quickgraph.
- Minimum_spanning_tree wikiPageExternalLink eisner.mst-tutorial.pdf.
- Minimum_spanning_tree wikiPageExternalLink minimum-spanning-tree.shtml.
- Minimum_spanning_tree wikiPageID "41795".
- Minimum_spanning_tree wikiPageRevisionID "605597754".
- Minimum_spanning_tree hasPhotoCollection Minimum_spanning_tree.
- Minimum_spanning_tree subject Category:Polynomial-time_problems.
- Minimum_spanning_tree subject Category:Spanning_tree.
- Minimum_spanning_tree type Abstraction100002137.
- Minimum_spanning_tree type Attribute100024264.
- Minimum_spanning_tree type Condition113920835.
- Minimum_spanning_tree type Difficulty114408086.
- Minimum_spanning_tree type Polynomial-timeProblems.
- Minimum_spanning_tree type Problem114410605.
- Minimum_spanning_tree type State100024720.
- Minimum_spanning_tree comment "Given a connected, undirected graph, a spanning tree of that graph is a subgraph that is a tree and connects all the vertices together. A single graph can have many different spanning trees. We can also assign a weight to each edge, which is a number representing how unfavorable it is, and use this to assign a weight to a spanning tree by computing the sum of the weights of the edges in that spanning tree.".
- Minimum_spanning_tree label "Arbre couvrant de poids minimal".
- Minimum_spanning_tree label "Minimaal opspannende boom".
- Minimum_spanning_tree label "Minimalne drzewo rozpinające".
- Minimum_spanning_tree label "Minimum spanning tree".
- Minimum_spanning_tree label "Árbol recubridor mínimo".
- Minimum_spanning_tree label "Árvore de extensão mínima".
- Minimum_spanning_tree label "Минимальное остовное дерево".
- Minimum_spanning_tree label "最小生成树".
- Minimum_spanning_tree sameAs Ελάχιστο_γεννητικό_δέντρο.
- Minimum_spanning_tree sameAs Árbol_recubridor_mínimo.
- Minimum_spanning_tree sameAs Arbre_couvrant_de_poids_minimal.
- Minimum_spanning_tree sameAs Minimaal_opspannende_boom.
- Minimum_spanning_tree sameAs Minimalne_drzewo_rozpinające.
- Minimum_spanning_tree sameAs Árvore_de_extensão_mínima.
- Minimum_spanning_tree sameAs m.0bh75.
- Minimum_spanning_tree sameAs Q240464.
- Minimum_spanning_tree sameAs Q240464.
- Minimum_spanning_tree sameAs Minimum_spanning_tree.
- Minimum_spanning_tree wasDerivedFrom Minimum_spanning_tree?oldid=605597754.
- Minimum_spanning_tree depiction Minimum_spanning_tree.svg.
- Minimum_spanning_tree isPrimaryTopicOf Minimum_spanning_tree.
