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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Obstructions to partitions of chordal graphs
TL;DR: All small matrices M are classified according to whether M -partitionable graphs have finitely or infinitely many minimal chordal obstructions, and whether they admit a polynomial time recognition algorithm or are NP-complete (for all matrices of size less than five).
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Distance problems within Helly graphs and $k$-Helly graphs
TL;DR: It is proved that a central vertex and all the medians in an $n$-vertex $m$-edge Helly graph can be computed w.h.p. in $\tilde{\cal O}(m\sqrt{n})$ time.
Book ChapterDOI
A Compact Data Structure and Parallel Algorithms for Permutation Graphs
TL;DR: Starting from a permutation of {0, ..., n−1} a compact data structure is obtained that allows to obtain the associated permutation graph and the transitive closure and reduction of the associated order of dimension 2 efficiently.
Parallel VLSI synthesis
TL;DR: The P-hardness results make it unlikely, however, that the exact parallel equivalent of a local search heuristic will be found that can find even a local minimum-cost solution in polylogarithmic time.
Journal ArticleDOI
On the S-labeling Problem
TL;DR: Basic properties of any optimal S-labeling of a graph G are proved, and the S- Labeling problem is polynomial-time solvable for split graphs.
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.