My question is regarding the algebraic formulation for packing problems in graphs.
Taking an example, suppose I am interested in the problem of finding if there is a packing of k edge disjoint triangles in a given input (undirected) graph. I am aware of techniques that approach this problem combinatorially. Is there a way to frame this problem algebraically?
Also, in context of graph theory, are algebraic methods less powerful when compared to combinatorial methods? Or is there any particular intuition that governs which approach is more effective in certain problems?
I apologize if my question sounds too general. The purpose of this question is to try and form an understanding of algebraic vs combinatorial methods in the context of graph theory.