Let G be a graph with order n, and let k be an integer with 1 ≤ k ≤ n/3. In this article, we show that if σ2(G) ≥ n + k − 1, then for any stable set S ⊆ V (G )w ith|S| = k, there exists a 2-factor with precisely k cycles C1 ,...,C k such that |V (Ci) ∩ S| =1f or all 1≤ i ≤ k and at most one of the cycles Ci has length strictly greater than three. The lower bound on σ2 is best possible.
['Shijya Chiba', 'Yoshimi Egawa', 'Kiyoshi Yoshimoto']
A 2-factor in which each cycle contains a vertex in a specified stable set