Packing and counting arbitrary Hamilton cycles in random digraphs
نویسندگان
چکیده
منابع مشابه
Packing 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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A Hamilton cycle in a digraph is a cycle passes through all the vertices, where all the arcs are oriented in the same direction. The problem of finding Hamilton cycles in directed graphs is well studied and is known to be hard. One of the main reasons for this, is that there is no general tool for finding Hamilton cycles in directed graphs comparable to the so called Posá ‘rotationextension’ te...
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Let n be sufficiently large and suppose that G is a digraph on n vertices where every vertex has inand outdegree at least n/2. We show that G contains every orientation of a Hamilton cycle except, possibly, the antidirected one. The antidirected case was settled by DeBiasio and Molla, where the threshold is n/2 + 1. Our result is best possible and improves on an approximate result by Häggkvist ...
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ژورنال
عنوان ژورنال: Random Structures & Algorithms
سال: 2018
ISSN: 1042-9832,1098-2418
DOI: 10.1002/rsa.20796