BETA
Examples ofpathwidth
Dictionary> Examples ofpathwidth
pathwidthisn’t in the Cambridge Dictionary yet. You can help!
Add a definition
The class of graphs withpathwidthat most one requires two excluded minors.
From theCambridge English Corpus
Therefore, the degeneracy is at most equal to the treewidth and at most equal to thepathwidth.
From
This example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.Planar graphs that can be partitioned into nested cycles, and planar graphs of boundedpathwidth, have universal point sets of nearly-linear size.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.In particular the maximal graphs ofpathwidthone are exactly the caterpillar trees.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.For earlier approximation algorithms forpathwidth, see and.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.A maximalpathwidth- "k" graph must be either a "k" -path or a "k" -caterpillar, two special kinds of "k" -tree.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.The graphs with such drawings havepathwidththat is bounded by a function of "h" and "k".
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.Additionally, for several special classes of graphs, such as trees, thepathwidthmay be computed in polynomial time without dependence on "k".
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.Since path-decompositions are a special case of tree-decompositions, thepathwidthof any graph is greater than or equal to its treewidth.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.Many problems in graph algorithms may be solved efficiently on graphs of boundedpathwidth, by using dynamic programming on a path-decomposition of the graph.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.However, the best known lower bound on thepathwidthof cubic graphs is smaller, 0.082 "n".
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.Alternatively, thepathwidthmay be defined from interval graphs analogously to the definition of treewidth from chordal graphs.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.If this evader is invisible to the pursuers then the problem is equivalent to finding thepathwidthor vertex separation.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.Another parameter, the graph bandwidth, has an analogous definition from proper interval graphs, and is at least as large as thepathwidth.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.The complexity of a vortex is limited by a parameter called its depth, closely related topathwidth.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.The same dynamic programming method also can be applied to graphs with unboundedpathwidth, leading to algorithms that solve unparametrized graph problems in exponential time.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.Pathwidthand path-decompositions are closely analogous to treewidth and tree decompositions.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.As a consequence, thepathwidthof a graph is always at least as large as its treewidth, but it can only be larger by a logarithmic factor.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.It remains open whether thepathwidthof a planar graph and its dual are always within a constant factor of each other in the remaining cases.
FromThis example is from Wikipedia and may be reused under a CC BY-SA license.
Wikipedia
This example is from Wikipedia and may be reused under a CC BY-SA license.These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
- Collocations with history
- Collocations with hitter
- Collocations with hockey
- Collocations with holder
- Collocations with hole
- Collocations with holiday
- Collocations with home
- Collocations with honour
- Collocations with hope
- Collocations with horizon
- Collocations with hospice
- Collocations with hospital
- Collocations with host
- Collocations with hostility
- Collocations with hotel
- Collocations with hour
- Collocations with house
- Collocations with household
- Collocations with hub
- Collocations with hull
- Collocations with humanity
- Collocations with humidity
- Collocations with humour
- Collocations with hunter
- Collocations with hurdle