Gordana Manić ; Yoshiko Wakabayashi - Packing triangles in low degree graphs and indifference graphs

dmtcs:3408 - Discrete Mathematics & Theoretical Computer Science, January 1, 2005, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05) - https://doi.org/10.46298/dmtcs.3408
Packing triangles in low degree graphs and indifference graphsArticle

Authors: Gordana Manić 1; Yoshiko Wakabayashi ORCID1

  • 1 Instituto de Matemática e Estatística

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 guarantee known so far for these problems has ratio $3/2 + ɛ$, a result that follows from a more general algorithm for set packing obtained by Hurkens and Schrijver in 1989. 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.


Volume: DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Section: Proceedings
Published on: January 1, 2005
Imported on: May 10, 2017
Keywords: triangle packing,approximation algorithm,polynomial algorithm,low degree graph,indifference graph,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]

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