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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Journal ArticleDOI
List Homomorphisms to Reflexive Graphs
Tomás Feder,Pavol Hell +1 more
TL;DR: A polynomial time algorithm is given to solve the problem when the input graph is an interval graph and it is argued that the complexity of certain other modifications of the problem are likely to be difficult to classify.
Proceedings Article
Graph sandwich problems.
TL;DR: Concentrating mainly on properties characterizing subfamilies of perfect graphs, polynomial algorithms for several properties are given and NP-completeness proofs are given for comparability graphs, permutation graphs, and several other families.
BookDOI
Edge Ideals: Algebraic and Combinatorial Properties
Susan Morey,Rafael H. Villarreal +1 more
TL;DR: A survey of algebraic and combinatorial properties of R/I(C) and C, respectively, can be found in this paper, where the authors give a criterion to estimate the regularity of the ideal of vertex covers of C. They also examine the associated primes of powers of edge ideals and show that these sets form an ascending chain.
Proceedings ArticleDOI
A characterization of the (natural) graph properties testable with one-sided error
Noga Alon,Asaf Shapira +1 more
TL;DR: It is shown that a graph property P has an oblivious one-sided error tester, if and only if P is (semi) hereditary, and infer that some of the most well studied graph properties, both in graph theory and computer science, are testable with one- sided error.
Journal ArticleDOI
Precoloring extension. I: Interval graphs
TL;DR: This question was motivated by practical problems in scheduling and VLSI theory and its complexity status for interval graphs and for graphs with a bounded treewidth is investigated.
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.