Let be the largest root of and In this article, we prove that for a positive integer , if G is an n -vertex connected graph with the spectral radius , then . The bound is sharp in the sense that for every positive integer , there are graphs H with and .Minjae Kim...
45 Yuval Peres Coloring a graph arising from a lacunary sequence 59:15 Vojtěch Rödl On two Ramsey type problems for Kt+1-free graphs 47:07 Vilmos Totik Erdős on polynomials And Ben Green The sum-free set constant is ⅓ 1:45:31 Tomasz Łuczak Threshold functions a historical ...
In this article, Temperley's bijection between spanning trees of the square grid on the one hand, and perfect matchings (also known as dimer coverings) of the square grid on the other, is extended to the setting of general planar directed (and undirected) graphs, where edges carry nonnegativ...
Let G be a fixed graph with largest (adjacency matrix) eigenvalue lambda(0) and with its universal cover having spectral radius p. W show that a random cov... Friedman,Joel - 《Duke Mathematical Journal》 被引量: 103发表: 2003年 Perfect Matchings in Random Graphs With Prescribed Minimal ...
This paper characterizes the graphs in G n , ν and G n , ν with the maximum spectral radius, and establishes a lower bound for the spectral radius of graphs of order n to guarantee that their fractional matching numbers are at least τ 1 2 . In addition, we explore the relationship ...
In this paper, we establish tight lower bounds on the size and the spectral radius ofGto guarantee thatGhas a fractional perfect matching, respectively. In addition, we investigate the relationship between fractional perfect matching andP2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\use...
nk2. As a result, we proveα′(G)≥nd2λ1(G)2+d2; we characterize when equality holds in the bound.doi:10.1016/j.ejc.2016.02.004Suil OElsevier LtdEuropean Journal of CombinatoricsS. O, Spectral radius and fractional matchings in graphs, European J. Combin. 55 (2016) 144-148....
O [Spectral\nradius and matchings in graphs, Linear Algebra Appl. 614 (2021) 316--324],\nwhich gives a sufficient condition for the existence of a perfect matching in a\ngraph in terms of the adjacency spectral radius.Yanhua ZhaoXueyi Huang...
Spectral radiusPerfect matchingLet U +(2k) be the set of all unicyclic graphs on 2k (k⩾2) vertices with perfect matchings. Let U 1 2 k be the graph on 2 k vertices obtained from C 3 by attaching a pendant edge and k−2 paths of length 2 at one vertex of C 3; Let U 2 ...
On the spectral radius of unicyclic graphs with perfect matchingsdoi:10.1016/S0024-3795(03)00394-XLet script capital U sign+(2k) be the set of all unicyclic graphs on 2k(k ≥ 2) vertices with perfect matchings. Let U12k be the graph on 2k vertices obtained from C3 by attaching a ...