Symmetric Hamilton Cycle Decompositions of Complete Multigraphs
V. Chitra ; A. Muthusamy
Discussiones Mathematicae Graph Theory, Tome 33 (2013), p. 695-707 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

Let n ≥ 3 and ⋋ ≥ 1 be integers. Let ⋋Kn denote the complete multigraph with edge-multiplicity ⋋. In this paper, we show that there exists a symmetric Hamilton cycle decomposition of ⋋K2m for all even ⋋ ≥ 2 and m ≥ 2. Also we show that there exists a symmetric Hamilton cycle decomposition of ⋋K2m − F for all odd ⋋ ≥ 3 and m ≥ 2. In fact, our results together with the earlier results (by Walecki and Brualdi and Schroeder) completely settle the existence of symmetric Hamilton cycle decomposition of ⋋Kn (respectively, ⋋Kn − F, where F is a 1-factor of ⋋Kn) which exist if and only if ⋋(n − 1) is even (respectively, ⋋(n − 1) is odd), except the non-existence cases n ≡ 0 or 6 (mod 8) when ⋋ = 1

Publié le : 2013-01-01
EUDML-ID : urn:eudml:doc:267866 
@article{bwmeta1.element.doi-10_7151_dmgt_1687,
     author = {V. Chitra and A. Muthusamy},
     title = {Symmetric Hamilton Cycle Decompositions of Complete Multigraphs},
     journal = {Discussiones Mathematicae Graph Theory},
     volume = {33},
     year = {2013},
     pages = {695-707},
     zbl = {1297.05138},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1687}
}

V. Chitra; A. Muthusamy. Symmetric Hamilton Cycle Decompositions of Complete Multigraphs. Discussiones Mathematicae Graph Theory, Tome 33 (2013) pp. 695-707. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1687/

[1] J. Akiyama, M. Kobayashi and G. Nakamura, Symmetric Hamilton cycle decompositions of the complete graph, J. Combin. Des. 12 (2004) 39-45. doi:10.1002/jcd.10066[Crossref] | Zbl 1031.05100

[2] B. Alspach, The wonderful Walecki construction, Bull. Inst. Combin. Appl. 52 (2008) 7-20. | Zbl 1157.05035

[3] J. Bosák, Decompositions of Graphs (Kluwer Academic Publishers, 1990). 4] R.A. Brualdi and M.W. Schroeder, Symmetric Hamilton cycle decompositions of complete graphs minus a 1-factor , J. Combin. Des. 19 (2011) 1-15. doi:10.1002/jcd.20257[Crossref]

[5] M. Buratti, S. Capparelli and A. Del Fra, Cyclic Hamiltonian cycle systems of the -fold complete and cocktail party graph, European J. Combin. 31 (2010) 1484-1496. doi:10.1016/j.ejc.2010.01.004[Crossref][WoS] | Zbl 1222.05141

[6] M. Buratti and A. Del Fra, Cyclic Hamiltonian cycle systems of the complete graph, Discrete Math. 279 (2004) 107-119. doi:10.1016/S0012-365X(03)00267-X[Crossref][WoS] | Zbl 1034.05030

[7] M. Buratti and F. Merola, Dihedral Hamiltonian cycle system of the cocktail party graph, J. Combin. Des. 21 (2013) 1-23. doi:10.1002/jcd.21311[WoS][Crossref] | Zbl 1260.05118

[8] A.J.W. Hilton, Hamiltonian decompositions of complete graphs, J. Combin. Theory (B) 36 (1984) 125-134. doi:10.1016/0095-8956(84)90020-0[Crossref]

[9] H. Jordon and J. Morris, Cyclic hamiltonian cycle systems of the complete graph minus a 1-factor , Discrete Math. 308 (2008) 2440-2449. doi:10.1016/j.disc.2007.05.009[Crossref][WoS] | Zbl 1172.05332

[10] D.E. Lucas, Recreations Mathematiques, Vol.2 (Gauthiers Villars, Paris, 1982). | Zbl 0088.00101