A polynomial time algorithm for the triangle packing problem on interval graphs - Myung, Young-Soo (Discrete Applied Mathematics, 2024)
The triangle packing problem (TPP) is to find the maximum number of pairwise vertex disjoint triangles in a given graph. The TPP is NP-complete in a general graph and even so when a given graph is restricted to a chordal graph. On the other hand, the TPP can be solved in polynomial time for unit interval graphs. For this reason, it is a well-known open problem to prove whether there exists a polynomial time algorithm solving the TPP on interval graphs. In this paper, we give an answer to the problem.