Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 1-12 |
| Number of pages | 12 |
| Journal | Combinatorics Probability and Computing |
| Volume | 9 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2000 |