Independent packings in structured graphs

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