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- Induced_path abstract "In the mathematical area of graph theory, an induced path in an undirected graph G is a path that is an induced subgraph of G. That is, it is a sequence of vertices in G such that each two adjacent vertices in the sequence are connected by an edge in G, and each two nonadjacent vertices in the sequence are not connected by any edge in G. An induced path is sometimes called a snake, and the problem of finding long induced paths in hypercube graphs is known as the snake-in-the-box problem.Similarly, an induced cycle is a cycle that is an induced subgraph of G; induced cycles are also called chordless cycles or (when the length of the cycle is four or more) holes. An antihole is a hole in the complement of G, i.e., an antihole is a complement of a hole.The length of the longest induced path in a graph has sometimes been called the detour number of the graph; for sparse graphs, having bounded detour number is equivalent to having bounded tree-depth. The induced path number of a graph G is the smallest number of induced paths into which the vertices of the graph may be partitioned, and the closely related path cover number of G is the smallest number of induced paths that together include all vertices of G. The girth of a graph is the length of its shortest cycle, but this cycle must be an induced cycle as any chord could be used to produce a shorter cycle; for similar reasons the odd girth of a graph is also the length of its shortest odd induced cycle.".
- Induced_path thumbnail Snakeinthebox.svg?width=300.
- Induced_path wikiPageExternalLink citation.cfm?id=982792.982920.
- Induced_path wikiPageExternalLink cyclecut.pdf.
- Induced_path wikiPageExternalLink KMT_preprocWG.ps.
- Induced_path wikiPageExternalLink BFHmrank.pdf.
- Induced_path wikiPageExternalLink splitting.pdf.
- Induced_path wikiPageExternalLink cliqueinap.ps.
- Induced_path wikiPageID "7714430".
- Induced_path wikiPageLength "11900".
- Induced_path wikiPageOutDegree "26".
- Induced_path wikiPageRevisionID "681977533".
- Induced_path wikiPageWikiLink Block_graph.
- Induced_path wikiPageWikiLink Category:Graph_theory_objects.
- Induced_path wikiPageWikiLink Chordal_graph.
- Induced_path wikiPageWikiLink Cograph.
- Induced_path wikiPageWikiLink Complement_(graph_theory).
- Induced_path wikiPageWikiLink Complement_graph.
- Induced_path wikiPageWikiLink Complete_graph.
- Induced_path wikiPageWikiLink Cycle_graph.
- Induced_path wikiPageWikiLink Dense_graph.
- Induced_path wikiPageWikiLink Distance-hereditary_graph.
- Induced_path wikiPageWikiLink Even-hole-free_graph.
- Induced_path wikiPageWikiLink Girth_(graph_theory).
- Induced_path wikiPageWikiLink Glossary_of_graph_theory.
- Induced_path wikiPageWikiLink Graph_theory.
- Induced_path wikiPageWikiLink Hypercube_graph.
- Induced_path wikiPageWikiLink Independent_set_(graph_theory).
- Induced_path wikiPageWikiLink Induced_subgraph.
- Induced_path wikiPageWikiLink Mathematics.
- Induced_path wikiPageWikiLink Mihalis_Yannakakis.
- Induced_path wikiPageWikiLink Path_(graph_theory).
- Induced_path wikiPageWikiLink Perfect_graph.
- Induced_path wikiPageWikiLink Snake-in-the-box.
- Induced_path wikiPageWikiLink Sparse_graph.
- Induced_path wikiPageWikiLink Tree-depth.
- Induced_path wikiPageWikiLink Tree_(graph_theory).
- Induced_path wikiPageWikiLink Triangle-free_graph.
- Induced_path wikiPageWikiLink Trivially_perfect_graph.
- Induced_path wikiPageWikiLink File:Snakeinthebox.svg.
- Induced_path wikiPageWikiLinkText "Induced path".
- Induced_path wikiPageWikiLinkText "induced 3-cycle".
- Induced_path wikiPageWikiLinkText "induced cycle".
- Induced_path wikiPageWikiLinkText "induced cycles".
- Induced_path wikiPageWikiLinkText "induced path".
- Induced_path hasPhotoCollection Induced_path.
- Induced_path wikiPageUsesTemplate Template:Cite_book.
- Induced_path wikiPageUsesTemplate Template:Cite_conference.
- Induced_path wikiPageUsesTemplate Template:Cite_journal.
- Induced_path wikiPageUsesTemplate Template:Harvtxt.
- Induced_path wikiPageUsesTemplate Template:Refbegin.
- Induced_path wikiPageUsesTemplate Template:Refend.
- Induced_path wikiPageUsesTemplate Template:Reflist.
- Induced_path subject Category:Graph_theory_objects.
- Induced_path hypernym Path.
- Induced_path type Place.
- Induced_path type Object.
- Induced_path comment "In the mathematical area of graph theory, an induced path in an undirected graph G is a path that is an induced subgraph of G. That is, it is a sequence of vertices in G such that each two adjacent vertices in the sequence are connected by an edge in G, and each two nonadjacent vertices in the sequence are not connected by any edge in G.".
- Induced_path label "Induced path".
- Induced_path sameAs 誘導パス.
- Induced_path sameAs m.0269q5c.
- Induced_path sameAs Порождённый_путь.
- Induced_path sameAs Породжений_шлях.
- Induced_path sameAs Q15704639.
- Induced_path sameAs Q15704639.
- Induced_path wasDerivedFrom Induced_path?oldid=681977533.
- Induced_path depiction Snakeinthebox.svg.
- Induced_path isPrimaryTopicOf Induced_path.