منابع مشابه
Regular factors in regular graphs
Katerinis, P., Regular factors in regular graphs, Discrete Mathematics 113 (1993) 269-274. Let G be a k-regular, (k I)-edge-connected graph with an even number of vertices, and let m be an integer such that 1~ m s k 1. Then the graph obtained by removing any k m edges of G, has an m-factor. All graphs considered are finite. We shall allow graphs to contain multiple edges and we refer the reader...
متن کاملRegular Factors in Graphs
Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek online verfügbar. Preface Many fields of mathematics are concerned with determining the smallest parts, or factors, of a certain kind, which make up a given object. Probably the best known examples in mathematics are the factorization of non-negative integers with prime numbers or the decomposition of polynomials. It was a pr...
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Let r and m be two integers such that r > m. Let H be a graph with order |H|, size e and maximum degree r such that 2e > |H|r−m. We find a best lower bound on spectral radius of graph H in terms of m and r. Let G be a connected r-regular graph of order |G| and k < r be an integer. Using the previous results, we find some best upper bounds (in terms of r and k) on the third largest eigenvalue th...
متن کاملOn Regular Factors in Regular Graphs with Small Radius
In this note we examine the connection between vertices of high eccentricity and the existence of k-factors in regular graphs. This leads to new results in the case that the radius of the graph is small (≤ 3), namely that a d-regular graph G has all k-factors, for k|V (G)| even and k ≤ d, if it has at most 2d+2 vertices of eccentricity > 3. In particular, each regular graph G of diameter ≤ 3 ha...
متن کاملCounting 1-Factors in Regular Bipartite Graphs
perfect matchings. (A perfect matching or 1-factor is a set of disjoint edges covering all vertices.) This generalizes a result of Voorhoeve [11] for the case k = 3, stating that any 3-regular bipartite graph with 2n vertices has at least ( 4 3) n perfect matchings. The base in (1) is best possible for any k: let αk be the largest real number such that any k-regular bipartite graph with 2n vert...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1993
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)90523-v