On the structure of graphs having a unique k-factor
نویسندگان
چکیده
In this paper, we prove that there is no r-regular graph (r ≥ 2) with a unique perfect matching. Also we show that a 2r-regular graph of order n has at least ( (r−k)r−k (r−k+1)r−k−1 )n 2k-factors, where k ≤ r. We investigate graphs with a unique [a, b]-factor and among other results, we prove that a connected graph with minimum degree at least 2 and a unique [1, 2]factor with regular components is an odd cycle.
منابع مشابه
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عنوان ژورنال:
- Australasian J. Combinatorics
دوره 69 شماره
صفحات -
تاریخ انتشار 2017