Improved non-approximability results for minimum vertex cover with density constraints

Andrea E.F. Clementi, Luca Trevisan
1999 Theoretical Computer Science  
We provide new non-approximabili~ results for the restrictjons of the MIN VERTEX COVER problem to bounded-degree, sparse and dense graphs. We show that for a suthciently large 3, the recent 1.16 lower bound proved by H&ad (1997) extends with negligible loss to graphs with bounded degree B. Then, we consider sparse graphs with no dense components (i.e. everywhere sparse graphs), and we show a similar result but with a better trade-off between non-approximability and spars&y. Finally, we observe
more » ... hat the MIN VERTEX COVER problem remains APX-complete when restricted to dense graph and thus recent techniques developed for several MAX SNP problems restricted to "dense" instances introduced by Arora et al. (1995) cannot be applied.
doi:10.1016/s0304-3975(97)00226-0 fatcat:4o2gvwapxzgrjlg4w2jixvhv44