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2015 | 35 | 1 | 73-79
Tytuł artykułu

On Decomposing Regular Graphs Into Isomorphic Double-Stars

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A double-star is a tree with exactly two vertices of degree greater than 1. If T is a double-star where the two vertices of degree greater than one have degrees k1+1 and k2+1, then T is denoted by Sk1,k2 . In this note, we show that every double-star with n edges decomposes every 2n-regular graph. We also show that the double-star Sk,k−1 decomposes every 2k-regular graph that contains a perfect matching.
Słowa kluczowe
Wydawca
Rocznik
Tom
35
Numer
1
Strony
73-79
Opis fizyczny
Daty
wydano
2015-02-01
otrzymano
2013-08-26
poprawiono
2014-02-07
zaakceptowano
2014-02-10
online
2015-02-06
Twórcy
  • Department of Mathematics Illinois State University Normal, Illinois 61790–4520, U.S.A., saad@ilstu.edu
autor
  • Department of Mathematics Illinois State University Normal, Illinois 61790–4520, U.S.A., ermet1mn@gmail.com
autor
  • Department of Mathematics Illinois State University Normal, Illinois 61790–4520, U.S.A., mikep@ilstu.edu
  • Department of Mathematics Illinois State University Normal, Illinois 61790–4520, U.S.A., tipnis@ilstu.edu
Bibliografia
  • [1] P. Adams, D. Bryant and M. Buchanan, A survey on the existence of G-designs, J. Combin. Des. 16 (2008) 373-410. doi:10.1002/jcd.20170[Crossref]
  • [2] D. Bryant and S. El-Zanati, Graph decompositions, in: Handbook of Combinatorial Designs, C.J. Colbourn and J.H. Dinitz (Ed(s)), (2nd Ed., Chapman & Hall/CRC, Boca Raton, 2007) 477-485.
  • [3] S.I. El-Zanati, M.J. Plantholt and S. Tipnis, On decomposing even regular multi- graphs into small isomorphic trees, Discrete Math. 325 (2014) 47-51. doi:10.1016/j.disc.2014.02.011[Crossref]
  • [4] J.A Gallian, A dynamic survey of graph labeling, Electron. J. Combin. 16 (2013) #DS6.
  • [5] R. Häggkvist, Decompositions of complete bipartite graphs, London Math. Soc. Lecture Note Ser. C.U.P., Cambridge 141 (1989) 115-147.
  • [6] M.S. Jacobson, M. Truszczy´nski and Zs. Tuza, Decompositions of regular bipartite graphs, Discrete Math. 89 (1991) 17-27. doi:10.1016/0012-365X(91)90396-J[Crossref]
  • [7] F. Jaeger, C. Payan and M. Kouider, Partition of odd regular graphs into bistars, Discrete Math. 46 (1983) 93-94. doi:10.1016/0012-365X(83)90275-3[Crossref]
  • [8] K.F. Jao, A.V. Kostochka and D.B. West, Decomposition of Cartesian products of regular graphs into isomorphic trees, J. Comb. 4 (2013) 469-490.
  • [9] A. Kotzig, Problem 1, in: Problem session, Proceedings of the Tenth Southeastern Conference on Combinatorics, Graph Theory and Computing, Congr. Numer. XXIV (1979) 913-915.
  • [10] G. Ringel, Problem 25, in: Theory of Graphs and its Applications, Proc. Symposium Smolenice 1963, Prague (1964), 162.
  • [11] H. Snevily, Combinatorics of Finite Sets, Ph.D. Thesis, (University of Illinois 1991).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_7151_dmgt_1779
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