Finding triangle-free 2-factors in general graphs

A 2-factor in a graph $G$ is a subset of edges $M$ such that every node of $G$ is incident with exactly two edges of $M$. Many results are known concerning 2-factors including a polynomial-time algorithm for finding 2-factors and a characterization of those graphs that have a 2-factor. The problem of finding a 2-factor in a graph is a relaxation of the NP-hard problem of finding a Hamilton cycle. A stronger relaxation is the problem of finding a triangle-free 2-factor, that is, a 2-factor whose edges induce no cycle of length 3. In this paper, we present a polynomial-time algorithm for the problem of finding a triangle-free 2-factor as well as a characterization of the graphs that have such a 2-factor and related min–max and augmenting path theorems.