A 2-factor in which each cycle contains a vertex in a specified stable set
نویسندگان
چکیده
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) with |S| = k, there exists a 2-factor with precisely k cycles C1, . . . , Ck such that |V (Ci) ∩ S| = 1 for 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.
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ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 46 شماره
صفحات -
تاریخ انتشار 2010