{
  "id": "1612.01965",
  "version": "v1",
  "published": "2016-12-06T19:54:12.000Z",
  "updated": "2016-12-06T19:54:12.000Z",
  "title": "Packing Directed and Hamilton Cycles Online",
  "authors": [
    "Michael Anastos",
    "Joseph Briggs"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Consider a directed analogue of the random graph process on $n$ vertices, where the $n(n-1)$ edges are ordered uniformly at random and revealed one at a time. It is known that w.h.p.\\@ the first digraph in this process with both in-degree and out-degree $\\geq q$ has a $[q]$-edge-coloring with a Hamilton cycle in each color. We show that this coloring can be constructed online, where each edge must be irrevocably colored as soon as it appears. In a similar fashion, for the \\emph{undirected} random graph process, we present an online $[n]$-edge-coloring algorithm which yields w.h.p.\\@ $q$ disjoint rainbow Hamilton cycles in the first graph of the process that contains $q$ disjoint Hamilton cycles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-06T19:54:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hamilton cycles online",
      "random graph process",
      "disjoint rainbow hamilton cycles",
      "disjoint hamilton cycles",
      "first digraph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}