Packing triangles in low degree graphs and indifference graphs

7Citations
Citations of this article
14Readers
Mendeley users who have this article in their library.

Abstract

We consider the problems of finding the maximum number of vertex-disjoint triangles (VTP) and edge-disjoint triangles (ETP) in a simple graph. Both problems are NP-hard. The algorithm with the best approximation ratio known so far for these problems has ratio 3 / 2 + ε, a result that follows from a more general algorithm for set packing obtained by Hurkens and Schrijver [On the size of systems of sets every t of which have an SDR, with an application to the worst-case ratio of heuristics for packing problems, SIAM J. Discrete Math. 2(1) (1989) 68-72]. We present improvements on the approximation ratio for restricted cases of VTP and ETP that are known to be APX-hard: we give an approximation algorithm for VTP on graphs with maximum degree 4 with ratio slightly less than 1.2, and for ETP on graphs with maximum degree 5 with ratio 4/3. We also present an exact linear-time algorithm for VTP on the class of indifference graphs. © 2007 Elsevier B.V. All rights reserved.

Cite

CITATION STYLE

APA

Manić, G., & Wakabayashi, Y. (2008). Packing triangles in low degree graphs and indifference graphs. Discrete Mathematics, 308(8), 1455–1471. https://doi.org/10.1016/j.disc.2007.07.100

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free