Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4949594 | Discrete Applied Mathematics | 2017 | 13 Pages |
Abstract
We consider the problem of deciding whether a k-colored graph can be completed to have a given property. We establish that, when k is not fixed, the completion problems for (Helly) circular-arc graphs, even (Helly) proper or (Helly) unit circular-arc graphs, are NP-complete. When k is fixed, in the case of completion to a (Helly) circular-arc graph, (Helly) proper circular-arc graph, or (Helly) unit circular-arc graph we fully classify the complexities of the problems. We also show that deciding whether a 3-colored graph can be completed to be strongly chordal can be done in O(n2) time. As a corollary of our results, the sandwich problems for Helly circular-arc graphs, Helly proper circular-arc graphs, and Helly unit circular-arc graphs are NP-complete.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Kathryn Cook, Elaine M. Eschen, R. Sritharan, Xiaoqiang Wang,