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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 cyclecut.pdf.
- Induced_path wikiPageExternalLink KMT_preprocWG.ps.
- Induced_path wikiPageExternalLink BFHmrank.pdf.
- Induced_path wikiPageExternalLink citation.cfm?id=982792.982920.
- Induced_path wikiPageExternalLink splitting.pdf.
- Induced_path wikiPageExternalLink cliqueinap.ps.
- Induced_path wikiPageID "7714430".
- Induced_path wikiPageRevisionID "540020947".
- Induced_path hasPhotoCollection Induced_path.
- Induced_path subject Category:Graph_theory_objects.
- Induced_path type GraphTheoryObjects.
- Induced_path type Object100002684.
- Induced_path type PhysicalEntity100001930.
- 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 label "Порождённый путь".
- Induced_path sameAs m.0269q5c.
- Induced_path sameAs Q15704639.
- Induced_path sameAs Q15704639.
- Induced_path sameAs Induced_path.
- Induced_path wasDerivedFrom Induced_path?oldid=540020947.
- Induced_path depiction Snakeinthebox.svg.
- Induced_path isPrimaryTopicOf Induced_path.
