On The Alspach Conjecture

@article{Balister2001OnTA,
  title={On The Alspach Conjecture},
  author={Paul N. Balister},
  journal={Combinatorics, Probability & Computing},
  year={2001},
  volume={10},
  pages={95-125}
}
It has been conjectured by Alspach [2] that given integers n and m1, . . . , mt with 3 ≤ mi ≤ n and ∑t i=1 mi = ( n 2 ) (n odd) or ∑t i=1 mi = ( n 2 )− n2 (n even) then one can pack Kn (n odd) or Kn minus a 1-factor (n even) with cycles of lengths m1, . . . , mt. In this paper we show that if the cycle lengths mi are bounded by some linear function of n and n is sufficiently large then this conjecture is true. 

From This Paper

Figures, tables, results, connections, and topics extracted from this paper.
8 Extracted Citations
12 Extracted References
Similar Papers

Referenced Papers

Publications referenced by this paper.
Showing 1-10 of 12 references

Research Problem 3

  • B. Alspach
  • Discrete Math. 36
  • 1981
Highly Influential
7 Excerpts

3

  • P. Adams, D. E. Bryant, A. Khodkar
  • 5)-cycle decompositions, J. Combin. Designs 6
  • 1998
Highly Influential
9 Excerpts

Even cycle decompositions of complete graphs minus a 1-factor

  • B. Alspach, S. Marshall
  • J. Combin. Designs 2
  • 1994
Highly Influential
5 Excerpts

Decompositions of large graphs and digraphs with high minimum degree

  • T. Gustavsson
  • Doctoral Dissertation, Dept. of Mathematics, Univ…
  • 1991
1 Excerpt

A lemma on cycle decomposition

  • R. Häggkvist
  • Ann. Discrete Math. 27
  • 1985
1 Excerpt

On the cycle decomposition of complete graphs (Chinese)

  • H. C. Sun
  • Nanjing Daxue Xuebao Ziran Kexue Ban 21
  • 1985

Graph factorization

  • R. G. Stanton, I. P. Goulden
  • general triple systems, and cyclic triple systems…
  • 1981
2 Excerpts

Decomposition of complete graphs into subgraphs isomorphic to a given graph

  • R. M. Wilson
  • Proc. 5th British Combinatorial Conference
  • 1975
1 Excerpt

Verification of conjecture of Th

  • E. S. O’Keefe
  • Skolem, Math. Scand
  • 1961
1 Excerpt

Similar Papers

Loading similar papers…