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Independent packings in structured graphs

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Abstract

Packing a maximum number of disjoint triangles into a given graph G is NP-hard, even for most classes of structured graphs. In contrast, we show that packing a maximum number of independent (that is, disjoint and nonadjacent) triangles is polynomial-time solvable for many classes of structured graphs, including weakly chordal graphs, asteroidal triple-free graphs, polygon-circle graphs, and interval-filament graphs. These classes contain other well-known classes such as chordal graphs, cocomparability graphs, circle graphs, circular-arc graphs, and outerplanar graphs. Our results apply more generally to independent packings by members of any family of connected graphs.

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Authors and Affiliations

  1. Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada, N2L 3C5

    Kathie Cameron

  2. School of Computing Science, Simon Fraser University, Burnaby, British Columbia, Canada, V5A 1S6

    Pavol Hell

Authors
  1. Kathie Cameron
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  2. Pavol Hell
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Correspondence to Kathie Cameron.

Additional information

Research of both authors is supported by the Natural Sciences and Engineering Research Council of Canada.

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Cameron, K., Hell, P. Independent packings in structured graphs. Math. Program. 105, 201–213 (2006). https://doi.org/10.1007/s10107-005-0649-5

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  • DOI: https://doi.org/10.1007/s10107-005-0649-5

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