East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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CIRCULANT DECOMPOSITIONS OF CERTAIN MULTIPARTITE GRAPHS INTO GREGARIOUS CYCLES OF A GIVEN LENGTH

  • Received : 2014.04.18
  • Accepted : 2014.05.07
  • Published : 2014.05.31
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Abstract

It is shown that, for an even positive integer m with $m{\geq}4$ and arbitrary positive integer k and t, the complete multipartite graph $K_{km+1(2t)}$ can be decomposed into edge-disjoint gregarious m-cycles in such a way that the decomposition is circulant.

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References

  1. B. Alspach and H. Gavlas, Cycle decompositions of $K_n$ and $K_n-I$. J. Combin. Theory Ser. B 81(2001), 77-99. https://doi.org/10.1006/jctb.2000.1996
  2. E. Billington and D. G. Hoffman, Decomposition of complete tripartite graphs into gre-garious 4-cycles. Discrete Math. 261(2003), 87-111. https://doi.org/10.1016/S0012-365X(02)00462-4
  3. E. Billington, D. G. Hoffman and C. A. Rodger, Resolvable gregarious cycle decompositions of complete equipartite graphs. Discrete Math. 308 (2008), no. 13, 2844-2853. https://doi.org/10.1016/j.disc.2006.06.047
  4. N. J. Cavenagh and E. J. Billington, Decompositions of complete multipartite graphs into cycles of even length. Graphs and Combinatorics 16(2000), 49-65. https://doi.org/10.1007/s003730050003
  5. E. J. Billington, B. R. Smith, and D. G. Hoffman, Equipartite gregarious 6- and 8-cycle systems. Discrete Mathematics 307(2007) 1659-1667. https://doi.org/10.1016/j.disc.2006.09.016
  6. J. R. Cho, A note on decomposition of complete equipartite graphs into gregarious 6-cycles. Bulletin of the Korean Mathematical Society 44(2007) 709-719. https://doi.org/10.4134/BKMS.2007.44.4.709
  7. J. R. Cho and R. J. Gould, Decompositions of complete multipartite graphs into gregar-ious 6-cycles using complete differences. Journal of the Korean Mathematical Society 45(2008) 1623-1634. https://doi.org/10.4134/JKMS.2008.45.6.1623
  8. J. R. Cho, J. M. Park, and Y. Sano, Edge-disjoint decompositions of complete multipar-tite graphs into gregarious long cycles. Computational Geometry and Graphs. Lecture Notes in Computer Science 8296(2012) 57-63.
  9. E. K. Kim, Y. M. Cho, and J. R. Cho, A difference set method for circulant decompo-sitions of complete partite graphs into gregarious 4-cycles. East Asian Mathematical Journal 26(2010) 655-670.
  10. J. Liu, A generalization of the Oberwolfach problem and Ct-factorizations of complete equipartite graphs. J. Combin. Designs 9(2000), 42-49.
  11. M. Sajna, Cycle decompositions III: complete graphs and fixed length cycles. J. Combin. Designs 10(2002), 27-78. https://doi.org/10.1002/jcd.1027
  12. M. Sajna, On decompositing $K_n-I$ into cycles of a fixed odd length. Discrete Math. 244(2002), 435-444. https://doi.org/10.1016/S0012-365X(01)00099-1
  13. B. R. Smith, Some gregarious cycle decompositions of complete equipartite graphs. Electron. J. Combin. 16(2009), no. 1, Research Paper 135, p17.
  14. D. Sotteau, Decomposition of $K(m,n)(K^*_{m,n}$ into cycles (circuits) of length 2k. J. Combin. Theory Ser B. 30(1981), 75-81. https://doi.org/10.1016/0095-8956(81)90093-9

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  1. A REMARK ON CIRCULANT DECOMPOSITIONS OF COMPLETE MULTIPARTITE GRAPHS BY GREGARIOUS CYCLES vol.33, pp.1, 2014, https://doi.org/10.7858/eamj.2017.007