## Tractability of Parameterized Completion Problems on Chordal, Strongly Chordal and Proper Interval Graphs (1994)

by
Haim Kaplan
,
Ron Shamir
,
Robert E. Tarjan

Citations: | 40 - 5 self |

### BibTeX

@MISC{Kaplan94tractabilityof,

author = {Haim Kaplan and Ron Shamir and Robert E. Tarjan},

title = {Tractability of Parameterized Completion Problems on Chordal, Strongly Chordal and Proper Interval Graphs},

year = {1994}

}

### Years of Citing Articles

### OpenURL

### Abstract

We study the parameterized complexity of three NP-hard graph completion problems. The MINIMUM FILL-IN problem is to decide if a graph can be triangulated by adding at most k edges. We develop O(c m) and O(k mn + f(k)) algorithms for this problem on a graph with n vertices and m edges. Here f(k) is exponential in k and the constants hidden by the big-O notation are small and do not depend on k. In particular, this implies that the problem is fixed-parameter tractable (FPT). The PROPER