Small Maximal Independent Sets and Faster Exact Graph Coloring
Download:
unknown authors
http://www.ics.uci.edu/~eppstein/pubs/Epp-WADS-01.pdf
Add To MetaCart
Abstract:
Abstract. We show that, for any n-vertex graph G and integer parameter k, there are at most 3 4k−n 4 n−3k maximal independent sets I ⊂ G with |I | ≤ k, and that all such sets can be listed in time O(3 4k−n 4 n−3k). These bounds are tight when n/4 ≤ k ≤ n/3. As a consequence, we show how to compute the exact chromatic number of a graph in time O((4/3+3 4/3 /4) n) ≈ 2.4150 n, improving a previous O((1+3 1/3) n) ≈ 2.4422 n algorithm of Lawler (1976). 1
Citations
| 54 | On cliques in graphs – Moon, Moser - 1965 |
| 38 | 3-coloring in time O(1.3446 n ): a noMIS algorithm – Beigel, Eppstein - 1995 |
| 32 | A note on the complexity of the chromatic number problem – Lawler - 1986 |
| 30 | Improved algorithms for 3-coloring,3-edge-coloring, and constraint satisfaction, manuscript – Eppstein - 2000 |
| 19 | 3-coloring in time O(1.3289 n – Beigel, Eppstein |
| 7 | Deciding 3-Colourability in less than O(1:415 n ) Steps – Schiermeyer - 1994 |
| 2 | On stables in graphs – Croitoru - 1979 |
