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...
متن کاملPacking Arborescences
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...
متن کاملEgerváry Research Group on Combinatorial Optimization Packing Arborescences Packing Arborescences
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...
متن کاملMatroid-Based Packing of Arborescences
We provide the directed counterpart of a slight extension of Katoh and Tanigawa’s result [8] on rooted-tree decompositions with matroid constraints. Our result characterizes digraphs having a packing of arborescences with matroid constraints. It is a proper extension of Edmonds’ result [1] on packing of spanning arborescences and implies – using a general orientation result of Frank [4] – the a...
متن کاملPacking and counting arbitrary Hamilton cycles in random digraphs
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