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2015 | 35 | 4 | 629-639
Tytuł artykułu

Decomposition of Complete Multigraphs Into Stars and Cycles

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let k be a positive integer, Sk and Ck denote, respectively, a star and a cycle of k edges. λKn is the usual notation for the complete multigraph on n vertices and in which every edge is taken λ times. In this paper, we investigate necessary and sufficient conditions for the existence of the decomposition of λKn into edges disjoint of stars Sk’s and cycles Ck’s.
Słowa kluczowe
Wydawca
Rocznik
Tom
35
Numer
4
Strony
629-639
Opis fizyczny
Daty
wydano
2015-11-01
online
2015-11-10
Twórcy
  • LIRIS UMR 5205, CNRS, University of Lyon, Claude Bernard Lyon 1 University 43 Bd du 11 Novembre 1918, F-69622, Villeurbanne, France, fairouz.beggas@liris.cnrs.fr
  • LIRIS UMR 5205, CNRS, University of Lyon, Claude Bernard Lyon 1 University 43 Bd du 11 Novembre 1918, F-69622, Villeurbanne, France, hamamache.kheddouci@liris.cnrs.fr
Bibliografia
  • [1] A.A. Abueida and M. Daven, Multidesigns for graph-pairs of order 4 and 5, Graphs Combin. 19 (2003) 433-447. doi:10.1007/s00373-003-0530-3[Crossref]
  • [2] A.A. Abueida and M. Daven, Multidecompositions of the complete graph, Ars Com- bin. 72 (2004) 17-22.
  • [3] A.A. Abueida and T. O’Neil, Multidecomposition of λKm into small cycles and claws, Bull. Inst. Combin. Appl. 49 (2007) 32-40.
  • [4] A.A. Abueida and C. Lian, On the decompositions of complete graphs into cycles and stars on the same number of edges, Discuss. Math. Graph Theory 34 (2014) 113-125. doi:10.7151/dmgt.1719[Crossref][WoS]
  • [5] B. Alspach and H. Gavlas, Cycle decompositions of Kn and Kn − I, J. Combin. Theory, Ser. B 81 (2001) 77-99. doi:10.1006/jctb.2000.1996[Crossref]
  • [6] D. Bryant, D. Horsley, B. Maenhaut and B.R. Smith, Cycle decompositions of com- plete multigraphs, J. Combin. Des. 19 (2011) 42-69. doi:10.1002/jcd.20263[Crossref]
  • [7] V. Chitra and A. Muthusamy, Symmetric Hamilton cycle decompositions of complete multigraphs, Discuss. Math. Graph Theory 33 (2013) 695-707. doi:10.7151/dmgt.1687[WoS][Crossref]
  • [8] S. Cichacz, Decomposition of complete bipartite digraphs and even complete bipartite multigraphs into closed trails, Discuss. Math. Graph Theory 27 (2007) 241-249. doi:10.7151/dmgt.1358[Crossref]
  • [9] H.-C. Lee and J.-J. Lin, Decomposition of the complete bipartite graph with a 1- factor removed into cycles and stars, Discrete Math. 313 (2013) 2354-2358. doi:10.1016/j.disc.2013.06.014[WoS]
  • [10] Z. Liang and J. Guo, Decomposition of complete multigraphs into crown graphs, J. Appl. Math. Comput. 32 (2010) 507-517. doi:10.1007/s12190-009-0267-0[Crossref]
  • [11] H.M. Priyadharsini and A. Muthusamy, (Gm,Hm)-multifactorization of λKm, J. Combin. Math. Combin. Comput. 69 (2009) 145-150.
  • [12] M. Šajna, Cycle decompositions III: Complete graphs and fixed length cycles, J. Combin. Des. 10 (2002) 27-78. doi:10.1002/jcd.1027[Crossref]
  • [13] T.-W. Shyu, Decompositions of complete graphs into paths and cycles, Ars Combin. 97 (2010) 257-270.
  • [14] T.-W. Shyu, Decomposition of complete graphs into paths of length three and trian- gles, Ars Combin. 107 (2012) 209-224.
  • [15] T.-W. Shyu, Decomposition of complete graphs into cycles and stars, Graphs Com- bin. 29 (2013) 301-313. doi:10.1007/s00373-011-1105-3[Crossref]
  • [16] T.-W. Shyu, Decomposition of complete bipartite graphs into paths and stars with same number of edges, Discrete Math. 313 (2013) 865-871. doi:10.1016/j.disc.2012.12.020[Crossref]
  • [17] D. Sotteau, Decomposition of Km,n (K(*) m,n) into cycles (circuits) of length 2k, J. Combin. Theory, Ser. B 30 (1981) 75-81. doi:10.1016/0095-8956(81)90093-9[Crossref]
  • [18] M. Tarsi, Decomposition of complete multigraphs into stars, Discrete Math. 26 (1979) 273-278. doi:10.1016/0012-365X(79)90034-7[Crossref]
  • [19] M. Tarsi, Decomposition of a complete multigraph into simple paths: Nonbalanced handcuffed designs, J. Combin. Theory, Ser. A 34 (1983) 60-70. doi:10.1016/0097-3165(83)90040-7[Crossref]
  • [20] R.M.Wilson, Decomposition of complete graphs into subgraphs isomorphic to a given graph, in: Proceedings of the 5th British Combinatorial Conference, Util. Math., Winnipeg, Congr. Numer. 15 (1976) 647-659.
  • [21] S. Yamamoto, H. Ikeda, S. Shige-eda, K. Ushio and N. Hamada, On claw- decomposition of complete graphs and complete bigraphs, Hiroshima Math. J. 5 (1975) 33-42.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1820
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