Non-Vertex-Balanced Factors in Random Graphs

Stefanie Gerke; Andrew McDowell

Non-Vertex-Balanced Factors in Random Graphs

Combinatorics 2013-04-11 v1

Authors: Stefanie Gerke , Andrew McDowell

Abstract

We prove part of a conjecture by Johansson, Kahn and Vu \cite{JKV} regarding threshold functions for the existence of an $H$ -factor in a random graph \gnp. We prove that the conjectured threshold function is correct for any graph $H$ which is not covered by its densest subgraphs. We also demonstrate that the main result of \cite{JKV} generalises to multigraphs, digraphs, and a multipartite model.

Keywords

hadwiger conjecture random graphs graph theory

Cite

@article{arxiv.1304.3000,
  title  = {Non-Vertex-Balanced Factors in Random Graphs},
  author = {Stefanie Gerke and Andrew McDowell},
  journal= {arXiv preprint arXiv:1304.3000},
  year   = {2013}
}

Comments

41 pages. Pre-print. arXiv admin note: text overlap with arXiv:0803.3406 by other authors

Non-Vertex-Balanced Factors in Random Graphs

Abstract

Keywords

Cite

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