English

Star-factors in graphs of high degree

Combinatorics 2016-11-16 v1

Abstract

We prove that every graph with sufficiently large minimum degree dd contains a spanning forest in which every component is a star of size at least dO~(d1/4)\sqrt{d} - \tilde O(d^{1/4}). This improves the result of Alon and Wormald and is optimal up to the lower order term.

Keywords

Cite

@article{arxiv.1611.04712,
  title  = {Star-factors in graphs of high degree},
  author = {Rajko Nenadov},
  journal= {arXiv preprint arXiv:1611.04712},
  year   = {2016}
}