Packing arborescences in random digraphs
نویسندگان
چکیده
منابع مشابه
Packing arborescences in random digraphs
We study the problem of packing arborescences in the random digraph D(n, p), where each possible arc is included uniformly at random with probability p = p(n). Let λ(D(n, p)) denote the largest integer λ ≥ 0 such that, for all 0 ≤ ` ≤ λ, we have ∑`−1 i=0(`− i)|{v : din(v) = i}| ≤ `. We show that the maximum number of arcdisjoint arborescences in D(n, p) is λ(D(n, p)) a.a.s. We also give tight e...
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In [7], Edmonds proved a fundamental theorem on packing arborescences that has become the base of several subsequent extensions. Recently, Japanese researchers found an unexpected further generalization which gave rise to many interesting questions about this subject [29], [20]. Another line of researches focused on covering intersecting families which generalizes Edmonds' theorems in a di eren...
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In [7], Edmonds proved a fundamental theorem on packing arborescences that has become the base of several subsequent extensions. Recently, Japanese researchers found an unexpected further generalization which gave rise to many interesting questions about this subject [29], [20]. Another line of researches focused on covering intersecting families which generalizes Edmonds' theorems in a di eren...
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We prove packing and counting theorems for arbitrarily oriented Hamilton cycles in D(n, p) for nearly optimal p (up to a logc n factor). In particular, we show that given t = (1 − o(1))np Hamilton cycles C1, . . . , Ct, each of which is oriented arbitrarily, a digraph D ∼ D(n, p) w.h.p. contains edge disjoint copies of C1, . . . , Ct, provided p = ω(log 3 n/n). We also show that given an arbitr...
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ژورنال
عنوان ژورنال: Electronic Notes in Discrete Mathematics
سال: 2017
ISSN: 1571-0653
DOI: 10.1016/j.endm.2017.07.015