Spectral radius and fractional matchings

in graphs

in graphs

Suil O

Georgia State University

Georgia State University

2014/12/23 Tuesday 4PM-5PM

Room 1409

Room 1409

A fractional matching of a graph G is a function f giving each edge a number between 0 and 1 so that \(\sum_{e \in \Gamma(v)} f(e) \le 1\) for each \(v \in V(G)\), where \(\Gamma(v)\) is the set of edges incident to v. The fractional matching number of G, written \(\alpha’_*(G)\), is the maximum of \(\sum_{e \in E(G)} f(e)\) over all fractional matchings f. Let G be an n-vertex graph with minimum degree d, and let \(\lambda_1(G)\) be the largest eigenvalue of G. In this talk, we prove that if k is a positive integer and \(\lambda_1(G) < d\sqrt{1+\frac{2k}{n-k}}[/latex], then [latex]\alpha'_*(G) > \frac{n-k}{2}\).

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