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Near 2-factorizations of 2K n : Cycles of even length

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Abstract

We show that the edges of the complete multigraph 2K mk+ 1 can be partitioned intomk + 1 factors, each the union ofmk-cycles, for all evenk, k ≥ 4.

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References

  1. Alspach, B., Häggkvist, R.: Some observations on the Oberwolfach problem. J. Graph Theory9, 177–187 (1985)

    Google Scholar 

  2. Alspach, B., Schellenberg, P., Stinson, D., Wagner, D.: The Oberwolfach problem and factors of uniform odd length cycles. Research Report No. 86-04, Dept. of Math. and Stats. Simon Fraser University.

  3. Bennett, F.E.: Conjugate orthogonal latin squares and Mendelsohn designs. Ars Comb.15, 51–62 (1985)

    Google Scholar 

  4. Bennett, F.E., Sotteau, D.: Almost resolvable decompositions ofK * n . J. Comb. Theory (B)30, 228–232 (1981)

    Google Scholar 

  5. Hanani, H.: On resolvable balanced incomplete block designs. J. Comb. Theory (A)17, 275–289 (1974)

    Google Scholar 

  6. Heinrich, K., Lindner, C.C., Rodger, C.A.: Almost resolvable decompositions of 2K n into cycles of odd length. J. Comb. Theory (A) (to appear)

  7. Horton, J.D., Roy, B.K., Schellenberg, P.J., Stinson, D.R.: On decomposing graphs into isomorphic uniform 2-factors, Ann. Discrete Math.27, 297–319 (1985)

    Google Scholar 

  8. Huang, C., Kotzig, A., Rosa, A.: On a variation of the Oberwolfach problem. Discrete Math.27, 261–277 (1979)

    Google Scholar 

  9. Lindner, C.C., Rodger, C.A.: Nesting and almost resolvability of pentagon systems. (preprint)

  10. Zhang, X.: On the existence of (v, 4, 1)-PMD. (preprint)

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Authors and Affiliations

  1. SUNY, 13126, Oswego, NY, USA

    James Burling

  2. SFU, V5A 1S6, Burnaby, BC, Canada

    Katherine Heinrich

Authors
  1. James Burling
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  2. Katherine Heinrich
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Additional information

Both authors are grateful to the Mathematics Department at Queen's University for the hospitality extended to them while visiting.

The author acknowledges the financial support of the Natural Sciences and Engineering Research Council of Canada under Grant No. A7829.

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Burling, J., Heinrich, K. Near 2-factorizations of 2K n : Cycles of even length. Graphs and Combinatorics 5, 213–221 (1989). https://doi.org/10.1007/BF01788673

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  • DOI: https://doi.org/10.1007/BF01788673

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