Large matchings from eigenvalues
نویسندگان
چکیده
منابع مشابه
Large matchings from eigenvalues
We find lower bounds on the difference between the spectral radius λ1 and the average degree 2e n of an irregular graph G of order n and size e. In particular, we show that, if n ≥ 4, then λ1 − 2e n > 1 n(∆ + 2) where ∆ is the maximum of the vertex degrees in G. Brouwer and Haemers found eigenvalue conditions sufficient to imply the existence of perfect matchings in regular graphs. Using the ab...
متن کاملPerfect matchings in regular graphs from eigenvalues
Throughout, G denotes a simple graph of order n (the number of vertices) and size e (the number of edges). The eigenvalues of G are the eigenvalues λi 1 Research partially supported by an NSERC postdoctoral fellowship. 2 Research supported by the Natural Sciences and Engineering Research Council of Canada. Email addresses: [email protected] (Sebastian M. Cioabă), [email protected] (D...
متن کاملMatchings in regular graphs from eigenvalues
Article history: Received 6 December 2006 Available online 26 July 2008
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In this note, we prove a sufficient condition for the existence of a perfect matching in a regular graph in terms of its eigenvalues and its expansion constant. We improve a recent result of Brouwer and Haemers. French version: Dans cette note, nous prouvons un état suffisant pour l’existence d’un assortiment parfait dans un graphe régulier en termes de ses valeurs propres et son constante d’ex...
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Let T + 2p be the set of all trees on 2p (p ≥ 1) vertices with perfect matchings. In this paper, we prove that for any tree T in T + 2p , the kth largest eigenvalue λk(T ) satisfies λk(T ) ≤ 1 2 “q ̊ p k ˇ − 1 + q ̊ p k ˇ + 3 ” (k = 1, 2, . . . , p). This upper bound is known to be best possible when k = 1. The set of trees obtained from a tree on p vertices by joining a pendent vertex to each ve...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2007
ISSN: 0024-3795
DOI: 10.1016/j.laa.2006.10.020