Normal hypergraphs and the perfect graph conjecture
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TL;DR: In this paper, it was shown that the complement of a perfect graph is perfect and a new proof for a related theorem of Berge and Las Vergnas was given for integer valued linear programming.
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About: This article is published in Discrete Mathematics. The article was published on 01 Jun 1972. and is currently open access. The article focuses on the topics: Perfect graph & Perfect graph theorem.
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Citations
The ellipsoid method and its consequences in combinatorial optimization
TL;DR: The method yields polynomial algorithms for vertex packing in perfect graphs, for the matching and matroid intersection problems, for optimum covering of directed cuts of a digraph, and for the minimum value of a submodular set function.
On the ratio of optimal integral and fractional covers
TL;DR: It is shown that the ratio of optimal integral and fractional covers of a hypergraph does not exceed 1 + log d, where d is the maximum degree and this theorem may replace probabilistic methods in certain circumstances.
1.3K
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
TL;DR: It is argued that many known interior point methods for linear programs can be transformed in a mechanical way to algorithms for SDP with proofs of convergence and polynomial time complexity carrying over in a similar fashion.
1K
Towards a theory of domination in graphs
TL;DR: The domatic number of a graph is defined and studied and it is seen that the theory of domination resembles the well known theory of colorings of graphs.
688
Edmonds polytopes and a hierarchy of combinatorial problems
TL;DR: It is proved that there is no upper bound on the rank of problems arising from the search for largest independent sets in graphs.
680
References
Blocking and anti-blocking pairs of polyhedra
TL;DR: Some of the main notions and theorems about blocking pairs of polyhedra and antiblocking pairs ofpolyhedra are described.
540
Sur un theorems du type könig pour hypergraphes
Claude Berge,Michel Las Vergnas +1 more
TL;DR: The purpose of t h i s paper is to present KSnig's theorem f o r b i p a r t i t e g raphs, and alsosome p r o p eR t i e s of unimodular m a t r i c e s, as well as some Classes of P e r f e c t Graphs.
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Anti-blocking polyhedra
TL;DR: In this paper, a theory parallel to that for blocking pairs of polyhedra is developed for anti-blocking pairs, and certain combinatorial results and problems are discussed in this framework.
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