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## Discussiones Mathematicae Graph Theory

2015 | 35 | 4 | 715-731
Tytuł artykułu

### Decomposition of Complete Bipartite Multigraphs Into Paths and Cycles Having k Edges

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EN
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EN
We give necessary and sufficient conditions for the decomposition of complete bipartite multigraph Km,n(λ) into paths and cycles having k edges. In particular, we show that such decomposition exists in Km,n(λ), when λ ≡ 0 (mod 2), [...] and k(p + q) = 2mn for k ≡ 0 (mod 2) and also when λ ≥ 3, λm ≡ λn ≡ 0(mod 2), k(p + q) =λ_mn, m, n ≥ k, (resp., m, n ≥ 3k/2) for k ≡ 0(mod 4) (respectively, for k ≡ 2(mod 4)). In fact, the necessary conditions given above are also sufficient when λ = 2.
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EN
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Tom
Numer
Strony
715-731
Opis fizyczny
Daty
wydano
2015-11-01
otrzymano
2014-08-09
poprawiono
2015-02-23
zaakceptowano
2015-02-23
online
2015-11-10
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autor
Bibliografia
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• [2] A.A. Abueida and M. Daven, Multidecompositions of the complete graph, Ars Combin. 72 (2004) 17-22.
• [3] A.A. Abueida, M. Daven and K.J. Roblee, Multidesigns of the λ-fold complete graph- pairs of orders 4 and 5, Australas. J. Combin. 32 (2005) 125-136.
• [4] A.A. Abueida and T. O’Neil, Multidecomposition of Km(λ) into small cycles and claws, Bull. Inst. Comb. Appl. 49 (2007) 32-40.
• [5] A.A. Abueida and C. Hampson, Multidecomposition of Kn − F into graph-pairs of order 5 where F is a Hamilton cycle or an (almost) 1-factor , Ars Combin. 97 (2010) 399-416.
• [6] A.A. Abueida and M. Daven, Multidecompositions of several graph products, Graphs Combin. 29 (2013) 315-326. doi:10.1007/s00373-011-1127-x[Crossref]
• [7] 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]
• [8] J.A. Bondy and U.R.S. Murty, Graph Theory with Applications (The Macmillan Press Ltd, New York, 1976).
• [9] C.C. Chou, C.M. Fu and W.C. Huang, Decomposition of Km,n into short cycles, Discrete Math. 197/198 (1999) 195-203. doi:10.1016/S0012-365X(99)90063-8[Crossref]
• [10] C.C. Chou and C.M. Fu, Decomposition of Km,n into 4-cycles and 2t-cycles, J. Comb. Optim. 14 (2007) 205-218. doi:10.1007/s10878-007-9060-x[Crossref]
• [11] S. Jeevadoss and A. Muthusamy, Sufficient condition for {C4, C2t}-decomposition of K2m,2n-An improved bound, S. Arumugam and B. Smyth (Eds.), Combinatorial Algorithms, IWOCA 2012, LNCS, (Springer-Verlag Berlin Heidelberg) 7643 (2012) 143-147.
• [12] S. Jeevadoss and A. Muthusamy, Decomposition of complete bipartite graphs into paths and cycles, Discrete Math. 331 (2014) 98-108. doi:10.1016/j.disc.2014.05.009[Crossref]
• [13] H.-C. Lee and Y.-P. Chu Multidecompositions of the balanced complete bipartite graphs into paths and stars, ISRN Combinatorics (2013). doi:10.1155/2013/398473[Crossref]
• [14] H.-C. Lee, Multidecompositions of complete bipartite graphs into cycles and stars, Ars Combin. 108 (2013) 355-364.
• [15] H.-C. Lee, Decomposition of complete bipartite graphs with a 1-factor removed into cycles and stars, Discrete Math. 313 (2013) 2354-2358. doi:10.1016/j.disc.2013.06.014[WoS]
• [16] D.G. Sarvate and L. Zhang, Decomposition of a λKv into equal number of K3s and P3s, Bull. Inst. Comb. Appl. 67 (2013) 43-48.
• [17] T.-W. Shyu, Decompositions of complete graphs into paths and cycles, Ars Combin. 97 (2010) 257-270.
• [18] T.-W. Shyu, Decompositions of complete graphs into paths and stars, Discrete Math. 330 (2010) 2164-2169. doi:10.1016/j.disc.2010.04.009[Crossref]
• [19] T.-W. Shyu, Decompositions of complete graphs into paths of length three and tri- angles, Ars Combin. 107 (2012) 209-224.
• [20] 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]
• [21] 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]
• [22] 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]
• [23] M. Truszczyński, Note on the decomposition of λKm,n(λK*m,n) into paths, Discrete Math. 55 (1985) 89-96. doi:10.1016/S0012-365X(85)80023-6 [Crossref]
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