Completing Colored Graphs to Meet a Target Property

Author(s)

Kathryn Cook, West Virginia University
Elaine M. Eschen, West Virginia University
R. Sritharan, University of DaytonFollow
Xiaoqiang Wang, West Virginia University

Document Type

Article

Publication Date

5-31-2017

Publication Source

Discrete Applied Mathematics

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.

Inclusive pages

39-51

ISBN/ISSN

0166-218X

Comments

Permission documentation on file.

Copyright

Copyright © 2017, Elsevier

Publisher

Elsevier

Volume

223

Peer Reviewed

yes

eCommons Citation

Cook, Kathryn; Eschen, Elaine M.; Sritharan, R.; and Wang, Xiaoqiang, "Completing Colored Graphs to Meet a Target Property" (2017). Computer Science Faculty Publications. 173.
https://ecommons.udayton.edu/cps_fac_pub/173