On unique k-factors and unique [1,k]-factors in graphs

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On the structure of graphs having a unique k-factor

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...

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On Theorems Equivalent with Kotzig's Result on Graphs with Unique 1-Factors

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ژورنال

عنوان ژورنال: Discrete Mathematics

سال: 2004

ISSN: 0012-365X

DOI: 10.1016/s0012-365x(03)00248-6