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A note on spanning Kr-cycles in random graphs

Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh PA 15213, USA

Special Issues: New advances in Combinatorics

We find a threshold for the existence of a collection of edge disjoint copies of Kr that form a cyclic structure and span all vertices of Gn,p. We use a recent result of Riordan to give a two line proof of the main result.
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Keywords spanning; Kr-cycle; threshold

Citation: Alan Frieze. A note on spanning Kr-cycles in random graphs. AIMS Mathematics, 2020, 5(5): 4849-4852. doi: 10.3934/math.2020309

References

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  • 3. K. Frankston, J. Kahn, B. Narayanan, et al. Thresholds versus fractional expectation thresholds, 2019. Available from: https://arxiv.org/pdf/1910.13433.pdf.
  • 4. A. M. Frieze, Loose Hamilton Cycles in Random 3-Uniform Hypergraphs, Electronic J. Comb., 17 (2010).
  • 5. A. Heckel, Random triangles in random graphs, 2018. Available from: https://arxiv.org/pdf/1802.08472.pdf.
  • 6. A. Johansson, J. Kahn and V. Vu, Factors in random graphs, Random Structures and Algorithms, 33 (2008), 1-28.    
  • 7. O. Riordan, Random cliques in random graphs, 2018. Available from: https://arxiv.org/pdf/1802.01948.pdf.

 

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