Balanced path decomposition of λ K n , n and λ K n , n *

Hung-Chih Lee; Chiang Lin

Czechoslovak Mathematical Journal (2009)

  • Volume: 59, Issue: 4, page 989-997
  • ISSN: 0011-4642

Abstract

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Let P k denote a path with k edges and ł K n , n denote the ł -fold complete bipartite graph with both parts of size n . In this paper, we obtain the necessary and sufficient conditions for ł K n , n to have a balanced P k -decomposition. We also obtain the directed version of this result.

How to cite

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Lee, Hung-Chih, and Lin, Chiang. "Balanced path decomposition of $\lambda K_{n,n}$ and $\lambda K^*_{n,n}$." Czechoslovak Mathematical Journal 59.4 (2009): 989-997. <http://eudml.org/doc/37971>.

@article{Lee2009,
abstract = {Let $P_k$ denote a path with $k$ edges and $łK_\{n,n\}$ denote the $ł$-fold complete bipartite graph with both parts of size $n$. In this paper, we obtain the necessary and sufficient conditions for $łK_\{n,n\}$ to have a balanced $P_k$-decomposition. We also obtain the directed version of this result.},
author = {Lee, Hung-Chih, Lin, Chiang},
journal = {Czechoslovak Mathematical Journal},
keywords = {path decomposition; balanced decomposition; complete bipartite graph; path decomposition; balanced decomposition; complete bipartite graph},
language = {eng},
number = {4},
pages = {989-997},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Balanced path decomposition of $\lambda K_\{n,n\}$ and $\lambda K^*_\{n,n\}$},
url = {http://eudml.org/doc/37971},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Lee, Hung-Chih
AU - Lin, Chiang
TI - Balanced path decomposition of $\lambda K_{n,n}$ and $\lambda K^*_{n,n}$
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 4
SP - 989
EP - 997
AB - Let $P_k$ denote a path with $k$ edges and $łK_{n,n}$ denote the $ł$-fold complete bipartite graph with both parts of size $n$. In this paper, we obtain the necessary and sufficient conditions for $łK_{n,n}$ to have a balanced $P_k$-decomposition. We also obtain the directed version of this result.
LA - eng
KW - path decomposition; balanced decomposition; complete bipartite graph; path decomposition; balanced decomposition; complete bipartite graph
UR - http://eudml.org/doc/37971
ER -

References

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  1. Bermond, J.-C., Cycles dans les graphes et G -configurations, Thesis, University of Paris XI (Orsay), Paris (1975). (1975) 
  2. Bosák, J., Decompositions of Graphs, Kluwer, Dordrecht, Netherlands (1990). (1990) MR1071373
  3. Huang, C., On Handcuffed designs, Dept. of C. and O. Research Report CORR75-10, University of Waterloo. 
  4. Hung, S. H. Y., Mendelsohn, N. S., 10.1016/0012-365X(77)90003-6, Discrete Math. 18 (1977), 23-33. (1977) Zbl0354.05016MR0447002DOI10.1016/0012-365X(77)90003-6
  5. Shyu, T.-W., Path decompositions of ł K n , n , Ars Comb. 85 (2007), 211-219. (2007) MR2359292
  6. Yu, M.-L., 10.1016/0012-365X(93)90305-D, Discrete Math. 122 (1993), 325-333. (1993) Zbl0792.05114MR1246687DOI10.1016/0012-365X(93)90305-D

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