منابع مشابه
Max k-cut and the smallest eigenvalue
Let G be a graph of order n and size m, and let mck (G) be the maximum size of a k-cut of G. It is shown that mck (G) k 1 k m μmin (G) n 2 , where μmin (G) is the smallest eigenvalue of the adjacency matrix of G. An infinite class of graphs forcing equality in this bound is constructed.
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The purpose of this semester project is to investigate the Spectral Bundle Method, which is a specialized subgradient method particularly suited for solving large scale semidefinite programs that can be cast as eigenvalue optimization problems of the form min y∈R aλmax(C − m ∑ i=1 Aiyi) + b T y, where C and Ai are given real symmetric matrices, b ∈ R allows to specify a linear cost term, and a ...
متن کاملBipartite Subgraphs And The Smallest Eigenvalue
Two results dealing with the relation between the smallest eigenvalue of a graph and its bipartite subgraphs are obtained. The first result is that the smallest eigenvalue μ of any non-bipartite graph on n vertices with diameter D and maximum degree ∆ satisfies μ > −∆ + 1 (D+1)n . This improves previous estimates and is tight up to a constant factor. The second result is the determination of th...
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We show how ’test’ vector fields may be used to give lower bounds for the Cheeger constant of a Euclidean domain (or Riemannian manifold with boundary), and hence for the lowest eigenvalue of the Dirichlet Laplacian on the domain. Also, we show that a continuous version of the classical Max Flow Min Cut Theorem for networks implies that Cheeger’s constant may be obtained precisely from such vec...
متن کاملThe smallest eigenvalue of the signless Laplacian
Recently the signless Laplacian matrix of graphs has been intensively investigated. While there are many results about the largest eigenvalue of the signless Laplacian, the properties of its smallest eigenvalue are less well studied. The present paper surveys the known results and presents some new ones about the smallest eigenvalue of the signless Laplacian.
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2012
ISSN: 0097-5397,1095-7111
DOI: 10.1137/090773714