论文信息 - Bipartite Subgraphs and the Smallest Eigenvalue

Bipartite 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 Δ satisfies μ ≥ −Δ + 1/(D+1)n. This improves previous estimates and is tight up to a constant factor. The second result is the determination of the precise approximation guarantee of the MAX CUT algorithm of Goemans and Williamson for graphs G = (V, E) in which the size of the max cut is at least A∣E∣, for all A between 0.845 and 1. This extends a result of Karloff.

Noga Alon | Benny Sudakov | N. Alon | B. Sudakov

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