Asymptotic Enumeration by Degree Sequence of Graphs of High Degree
نویسندگان
چکیده
منابع مشابه
Asymptotic Enumeration by Degree Sequence of Graphs of High Degree
We consider the estimation of the number of labelled simple graphs with degree sequence d1, d2, . . . , dn by using an n-dimensional Cauchy integral. For suffiently small and any c > 2 3 , an asymptotic formula is obtained when |di − d| < n for all i and d = d(n) satisfies min{d, n − d − 1} ≥ cn/ log n as n → ∞. These conditions include the degree sequences of almost all graphs, so our result g...
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We determine the asymptotic number of labelled graphs with a given degree sequence for the case where the maximum degree is o(|E(G)|). The previously best enumeration, by the first author, required maximum degree o(|E(G)|). In particular, if k = o(n), the number of regular graphs of degree k and order n is asymptotically (nk)! (nk/2)! 2nk/2(k!)n exp ( − 2 − 1 4 − k 3 12n + O(k/n) ) . Under slig...
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ある属性をもつ対象が存在するのか,また存在すれ ば何個存在するのかという問,すなわち数え上げは, 科学的考察の基本をなすものである.指定された性質 をもつ対象の数え上げに関する多くの研究が知られて いる.更に,個数を数え上げるだけではなく,実際にす べての対象を生成するという列挙問題についても,最 近の計算機の性能の向上とともに,多くの列挙問題が 実際に解けるようになりつつある.また,列挙問題を 主に扱った本が多数出版されている [3]~[5], [13], [14]. もし,指定された属性をもつグラフの列挙ができれば, 理論的には様々な予想に対して反例を探すことを試み るリストに利用でき,応用的にはそれらのグラフを入 力とするプログラムのテストデータとして利用でき る.既に多くの列挙アルゴリズムが知られている.例 えば,[1], [2], [9], [17]である. 本論文はグラフ...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 1990
ISSN: 0195-6698
DOI: 10.1016/s0195-6698(13)80042-x