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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Approximating the joint replenishment problem with deadlines
Tim Nonner,Alexander Souza +1 more
TL;DR: This work investigates the natural special case that each demand has a deadline until when it needs to be satisfied, and presents a randomized 5/3-approximation algorithm that proves that JRP with deadlines is APX-hard and extends the known hardness results by showing that J RP with linear delay cost functions is NP-hard.
Proceedings ArticleDOI
String graphs and incomparability graphs
Jacob Fox,János Pach +1 more
TL;DR: It is proved that for every ε>0 there exists δ>0 with the property that if C is a collection of curves whose string graph has at least ε |C|2 edges, then one can select a subcurve γ' of each γ ∈ C such that the string graph of the collection {γ':γ ∈� C} hasAt least δ |C |2 edges and is an incomparability graph.
Journal ArticleDOI
On the complexity of graph reconstruction
TL;DR: It is shown that Legitimate Deck, Preimage Construction, and Preimage Counting are solvable in polynomial time for graphs of bounded degree, partialk-trees for any fixedk, and graphs of bound genus, in particular for planar graphs.
Posted Content
Hypergraph Acyclicity Revisited
TL;DR: This work introduces new notions of alpha, beta, and gamma leaf that allow one to define new “rule-based” characterizations of each notion, and proves the equivalence between the numerous characterizations with a new, simpler proof in a self-contained manner.
Proceedings ArticleDOI
Efficient construction of unit circular-arc models
TL;DR: A characterization of UCA graphs which leads to linear time algorithms for recognizing UCA graph graphs and constructing UCA models is described and models whose extreme of the arcs correspond to integers of size O(n).
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.