Clique-width of path powers
نویسندگان
چکیده
منابع مشابه
Computing the Clique-Width of Large Path Powers in Linear Time via a New Characterisation of Clique-Width
Clique-width is one of the most important graph parameters, as many NP-hard graph problems are solvable in linear time on graphs of bounded clique-width. Unfortunately the computation of clique-width is among the hardest problems. In fact we do not know of any other algorithm than brute force for the exact computation of clique-width on any nontrivial large graph class. Another difficulty about...
متن کاملA Complete Characterisation of the Linear Clique-Width of Path Powers
A k-path power is the k-power graph of a simple path of arbitrary length. Path powers form a non-trivial subclass of proper interval graphs. Their clique-width is not bounded by a constant, and no polynomial-time algorithm is known for computing their clique-width or linear clique-width. We show that k-path powers above a certain size have linear clique-width exactly k + 2, providing the first ...
متن کاملThe NLC-width and clique-width for powers of graphs of bounded tree-width
The k-power graph of a graph G is a graphwith the same vertex set as G, in that two vertices are adjacent if and only if, there is a path between them in G of length at most k. A k-treepower graph is the k-power graph of a tree, a k-leaf-power graph is the subgraph of some k-tree-power graph induced by the leaves of the tree. We show that (1) every k-tree-power graph has NLC-width at most k + 2...
متن کاملGraph classes with and without powers of bounded clique-width
Clique-width is a graph parameter with many algorithmic applications. For a positive integer k, the k-th power of a graph G is the graph with the same vertex set as G, in which two distinct vertices are adjacent if and only if they are at distance at most k in G. Many graph algorithmic problems can be expressed in terms of graph powers. We initiate the study of graph classes of power-bounded cl...
متن کاملMulti-Clique-Width
Multi-clique-width is obtained by a simple modification in the definition of cliquewidth. It has the advantage of providing a natural extension of tree-width. Unlike clique-width, it does not explode exponentially compared to tree-width. Efficient algorithms based on multi-clique-width are still possible for interesting tasks like computing the independent set polynomial or testing c-colorabili...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2016
ISSN: 0166-218X
DOI: 10.1016/j.dam.2015.11.009