Some results on triangle partitions

TL;DR

This paper investigates the computational complexity of triangle packing problems across various graph classes, providing efficient algorithms for some and complexity results for others, including characterizations of specific graph types.

Contribution

It introduces new efficient algorithms for triangle packing in several graph classes and establishes NP-completeness results for others, along with characterizations of cobipartite graphs.

Findings

Efficient algorithms for triangle packing in colored permutation, complete multipartite, and distance-hereditary graphs.

NP-completeness of C_4-packing in bipartite graphs.

Characterization of cobipartite graphs with triangle partitions.

Abstract

We show that there exist efficient algorithms for the triangle packing problem in colored permutation graphs, complete multipartite graphs, distance-hereditary graphs, k-modular permutation graphs and complements of k-partite graphs (when k is fixed). We show that there is an efficient algorithm for C_4-packing on bipartite permutation graphs and we show that C_4-packing on bipartite graphs is NP-complete. We characterize the cobipartite graphs that have a triangle partition.