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H(n)-factors in random graphs

Author

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  • Yan, Yun-Zhi
  • Wang, Han-Xing
  • Wang, Jun
  • Yin, Xiang-Feng

Abstract

For graphs Gn on n vertices and H(n) on hn vertices, where hn divides n, an H(n)-factor of Gn is a spanning subgraph of Gn consisting of n/hn vertex disjoint copies of H(n). Our main result has supplied a lower bound (or upper bound) of p in the problem of determining the minimal (or maximal) probability p=p(n), for which almost surely random graph G(n;p) contains an (or contains no) H(n)-factor, where H(n) satisfies certain conditions. The bound of p for the same problem when H(n) is a fixed graph has been studied by Alon and Yuster and by Rucinski and by Krivelevich.

Suggested Citation

  • Yan, Yun-Zhi & Wang, Han-Xing & Wang, Jun & Yin, Xiang-Feng, 2008. "H(n)-factors in random graphs," Statistics & Probability Letters, Elsevier, vol. 78(11), pages 1255-1258, August.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:11:p:1255-1258
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