JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (4): 86-90.doi: 10.6040/j.issn.1671-9352.0.2017.652

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K4-factors in random graphs

ZHANG Wei-wei*, CAI Jian-sheng   

  1. School of Mathematics and Information Science, Weifang University, Weifang 261061, Shandong, China
  • Published:2019-04-08

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Abstract: For a graph G with n vertices, where 4 divides n, a K4-factor is a subgraph of G, consisting of(n)/4 vertex disjoint K4. The minimal probability p=p(n) for which a random graph G(n,p)almost surely contains a K4-factor. For p=O(n-0.44), the random graph G(n,p)almost surely contains a K4-factor.

Key words: random graphs, K4-factors, probabilistic method, Janson inequality

CLC Number: 

  • O157.5
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