Packing, Counting and Covering Hamilton cycles in random directed graphs

Asaf Ferber, Gal Kronenberg, Eoin Long

Research output: Contribution to journalArticlepeer-review

Abstract

A Hamilton cycle in a digraph is a cycle passing 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 'rotation-extension' technique for the undirected analogue. Here, we present a general and a very simple method, using known results, to attack problems of packing, counting and covering Hamilton cycles in random directed graphs, for every edge-probability p>logC(n)/n. Our results are asymptotically optimal with respect to all parameters and apply equally well to the undirected case.

Original languageEnglish
Pages (from-to)813-819
Number of pages7
JournalElectronic Notes in Discrete Mathematics
Volume49
DOIs
StatePublished - Nov 2015

Keywords

  • Directed graphs
  • Hamilton cycles
  • Random graphs

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