On the algorithmic complexity of twelve covering and independence parameters of graphs

Manlove, D.F. (1999) On the algorithmic complexity of twelve covering and independence parameters of graphs. Discrete Applied Mathematics, 91(1-3), pp. 155-175. (doi: 10.1016/S0166-218X(98)00147-4)

Abstract

The definitions of four previously studied parameters related to total coverings and total matchings of graphs can be restricted, thereby obtaining eight parameters related to covering and independence, each of which has been studied previously in some form. Here we survey briefly results concerning total coverings and total matchings of graphs, and consider the aforementioned 12 covering and independence parameters with regard to algorithmic complexity. We survey briefly known results for several graph classes, and obtain new NP-completeness results for the minimum total cover and maximum minimal total cover problems in planar graphs, the minimum maximal total matching problem in bipartite and chordal graphs, and the minimum independent dominating set problem in planar cubic graphs.

• Item Type: Articles
• Keywords: Covering; Independence; Total cover; Total matching; Independent domination
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Manlove, Professor David
• Authors: Manlove, D.F.
• Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
• College/School: College of Science and Engineering > School of Computing Science
• Research Group: Formal Analysis, Theory and Algorithms
• Journal Name: Discrete Applied Mathematics
• Publisher: Elsevier
• ISSN: 0166-218X
• Copyright Holders: ©1999 Published by Elsevier Science B.V.
• First Published: First published in Discrete Applied Mathematics 91(1-3):155-175
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher.