| 词汇 | pathwidth |
| 释义 | BETA Examples of pathwidthpathwidth isn’t in the Cambridge Dictionary yet. You can help! The class of graphs with pathwidth at most one requires two excluded minors. Therefore, the degeneracy is at most equal to the treewidth and at most equal to the pathwidth. From 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 bounded pathwidth, have universal point sets of nearly-linear size. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. In particular the maximal graphs of pathwidth one are exactly the caterpillar trees. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. For earlier approximation algorithms for pathwidth, see and. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. A maximal pathwidth- "k" graph must be either a "k" -path or a "k" -caterpillar, two special kinds of "k" -tree. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The graphs with such drawings have pathwidth that is bounded by a function of "h" and "k". From 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, the pathwidth may be computed in polynomial time without dependence on "k". From 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, the pathwidth of any graph is greater than or equal to its treewidth. From 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 bounded pathwidth, by using dynamic programming on a path-decomposition of the graph. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. However, the best known lower bound on the pathwidth of cubic graphs is smaller, 0.082 "n". From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Alternatively, the pathwidth may be defined from interval graphs analogously to the definition of treewidth from chordal graphs. From 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 the pathwidth or vertex separation. From 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 the pathwidth. From 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 to pathwidth. From 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 unbounded pathwidth, leading to algorithms that solve unparametrized graph problems in exponential time. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Pathwidth and path-decompositions are closely analogous to treewidth and tree decompositions. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. As a consequence, the pathwidth of a graph is always at least as large as its treewidth, but it can only be larger by a logarithmic factor. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. It remains open whether the pathwidth of a planar graph and its dual are always within a constant factor of each other in the remaining cases. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. |
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