Journal ArticleDOI
Weakly bipartite graphs and the Max-cut problem
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TLDR
It is shown that the max-cut problem can be solved in polynomial time for weakly bipartite graphs and an algorithm that computes a shortest path of even length is presented.About:
This article is published in Operations Research Letters.The article was published on 1981-10-01. It has received 165 citations till now. The article focuses on the topics: Complete bipartite graph & Chordal graph.read more
Citations
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BookDOI
Handbook of Semidefinite Programming
TL;DR: Conditions and an accurate semidefinite programming solver are described in The Journal of the SDPA family for solving large-scale SDPs and in Handbook on Semidefinitely Programming.
Journal ArticleDOI
An application of combinatorial optimization to statistical physics and circuit layout design
TL;DR: A cutting plane algorithm is designed based on a partial characterization of the cut polytope and used to solve max-cut problems on graphs with up to 1,600 nodes.
Journal ArticleDOI
A Mathematical Bibliography of Signed and Gain Graphs and Allied Areas
TL;DR: This is a bibliography of signed graphs and related mathematics, where work on weighted graphs are regarded as outside the scope of the bibliography — except (to some extent) when the author calls the weights "signs".
MonographDOI
Combinatorial optimization : packing and covering
TL;DR: In this article, the authors propose a method for decomposition of perfect graphs and matrices by k-sum decomposition by k -sum, which is based on the idea of odd cyclic cycles in graphs.
Journal ArticleDOI
Laplacian eigenvalues and the maximum cut problem
C. Delorme,Svatopluk Poljak +1 more
TL;DR: An eigenvalue upper boundϕ(G) on the maximum cut mc (G) of a weighted graph has several interesting properties that resemble the behaviour ofmc (G), and ϕ is subadditive with respect to amalgam, and additive withrespect to disjoint sum and 1-sum.
References
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Book
Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Journal ArticleDOI
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.
Journal ArticleDOI
Maximum matching and a polyhedron with 0,1-vertices
TL;DR: The emphasis in this paper is on relating the matching problem to the theory of continuous linear programming, and the algorithm described does not involve any "blind-alley programming" -which, essentially, amounts to testing a great many combinations.
Proceedings ArticleDOI
Node-and edge-deletion NP-complete problems
TL;DR: This paper shows that if &pgr; belongs to a rather broad class of properties then the node-deletion problem is NP-complete, and the same is true for several restrictions of it.