On unique k-factors and unique [1,k]-factors in graphs
نویسندگان
چکیده
منابع مشابه
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15 صفحه اولOn 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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We show that several known theorems on graphs and digraphs are equivalent. The list of equivalent theorems include Kotzig’s result on graphs with unique 1-factors, a lemma by Seymour and Giles, theorems on alternating cycles in edge-colored graphs, and a theorem on semicycles in digraphs. We consider computational problems related to the quoted results; all these problems ask whether a given (d...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2004
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(03)00248-6