Journal ArticleDOI
Algorithmic graph theory and perfect graphs
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This article is published in Order.The article was published on 1986-06-01. It has received 1324 citations till now. The article focuses on the topics: Trivially perfect graph & Perfect graph theorem.read more
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Independent Sets in Asteroidal Triple-Free Graphs
TL;DR: It is shown that there is an O(n4) time algorithm to compute the maximum weight of an independent set for AT-free graphs, and that the problems CLIQUE and PARTITION INTO CLIQUES remain NP-complete when restricted to AT- free graphs.
Journal ArticleDOI
On treewidth and minimum fill-in of asteroidal triple-free graphs
TL;DR: These algorithms yields polynomial time algorithms for the four NP-complete graph problems on any subclass of the asteroidal triple-free graphs that has a polynomially bounded number of minimal separators, as e.g. cocomparability graphs of bounded dimension and d-trapezoid graphs for any fixed d ⩾ 1.
Journal ArticleDOI
Exact Algorithms for Treewidth and Minimum Fill-In
TL;DR: It is shown that the treewidth and the minimum fill-in of an $n$-vertex graph can be computed in time $\mathcal{O}(1.8899^n)$ and the running time of the algorithms can be reduced to 1.4142 minutes.
Posted Content
The Interlace Polynomial of a Graph
TL;DR: It emerges that the interlace graph polynomial may be viewed as a special case of the MartinPolynomial of an isotropic system, which underlies its connections with the circuit partition polynometric and the Kauffman brackets of a link diagram.
Book
Partitions of graphs into one or two independent sets and cliques: Revised version
TL;DR: It is shown that it can be recognized in polynomial time whether the vertex set of a finite undirected graph can be partitioned into one or two independent sets and one orTwo cliques.
References
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Interval graphs and related topics
TL;DR: A more general paradigm for studying various classes of graphs is suggested which can be described as follows: when 9 is allowed to be an arbitrary family of sets, the class obtained as intersection graphs is all undirected graphs.