Brambles and independent packings in chordal graphs

An independent packing of triangles is a set of pairwise disjoint triangles, no two of which are joined by an edge. A triangle bramble is a set of triangles, every pair of which intersect or are joined by an edge. More generally, I consider independent packings and brambles of any specified connected graphs, not just triangles. I give a min–max theorem for the maximum number of graphs in an independent packing of any family of connected graphs in a chordal graph, and a dual min–max theorem for the maximum number of graphs in a bramble in a chordal graph.