Triangle decompositions of planar graphs
Christina M. Mynhardt, Christopher M. van Bommel · Discussiones Mathematicae Graph Theory · 2016
A multigraph G is triangle decomposable if its edge set can be partitioned into subsets, each of which induces a triangle of G, and rationally triangle decomposable if its triangles can be assigned rational weights such that for each edge e of G, the sum of the weights of the triangles that contain e equals 1.