# Decompositions of a complete multidigraph into almost arbitrary paths

Mariusz Meszka; Zdzisław Skupień

Discussiones Mathematicae Graph Theory (2012)

- Volume: 32, Issue: 2, page 357-372
- ISSN: 2083-5892

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topMariusz Meszka, and Zdzisław Skupień. "Decompositions of a complete multidigraph into almost arbitrary paths." Discussiones Mathematicae Graph Theory 32.2 (2012): 357-372. <http://eudml.org/doc/270814>.

@article{MariuszMeszka2012,

abstract = {For n ≥ 4, the complete n-vertex multidigraph with arc multiplicity λ is proved to have a decomposition into directed paths of arbitrarily prescribed lengths ≤ n - 1 and different from n - 2, unless n = 5, λ = 1, and all lengths are to be n - 1 = 4. For λ = 1, a more general decomposition exists; namely, up to five paths of length n - 2 can also be prescribed.},

author = {Mariusz Meszka, Zdzisław Skupień},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {complete digraph; multidigraph; tour girth; arbitrary path decomposition},

language = {eng},

number = {2},

pages = {357-372},

title = {Decompositions of a complete multidigraph into almost arbitrary paths},

url = {http://eudml.org/doc/270814},

volume = {32},

year = {2012},

}

TY - JOUR

AU - Mariusz Meszka

AU - Zdzisław Skupień

TI - Decompositions of a complete multidigraph into almost arbitrary paths

JO - Discussiones Mathematicae Graph Theory

PY - 2012

VL - 32

IS - 2

SP - 357

EP - 372

AB - For n ≥ 4, the complete n-vertex multidigraph with arc multiplicity λ is proved to have a decomposition into directed paths of arbitrarily prescribed lengths ≤ n - 1 and different from n - 2, unless n = 5, λ = 1, and all lengths are to be n - 1 = 4. For λ = 1, a more general decomposition exists; namely, up to five paths of length n - 2 can also be prescribed.

LA - eng

KW - complete digraph; multidigraph; tour girth; arbitrary path decomposition

UR - http://eudml.org/doc/270814

ER -

## References

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- [6] M. Meszka and Z. Skupień, Decompositions of a complete multidigraph into nonhamiltonian paths, J. Graph Theory 51 (2006) 82-91, doi: 10.1002/jgt.20122. Zbl1084.05054
- [7] M. Meszka and Z. Skupień, Long paths decompositions of a complete digraph of odd order, Congr. Numer. 183 (2006) 203-211.
- [8] M. Tarsi, Decomposition of a complete multigraph into simple paths: Nonbalanced handcuffed designs, J. Combin. Theory (A) 34 (1983) 60-70, doi: 10.1016/0097-3165(83)90040-7. Zbl0511.05024
- [9] T. Tillson, A Hamiltonian decomposition of $K{*}_{2m}$, 2m ≥ 8, J. Combin. Theory (B) 29 (1980) 68-74, doi: 10.1016/0095-8956(80)90044-1.

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