Decompositions of a complete multidigraph into almost arbitrary paths

• Autorzy: Mariusz Meszka , Zdzisław Skupień
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

complete digraph; multidigraph; tour girth; arbitrary path decomposition

Kategorie tematyczne

• 05C70: Factorization, matching, partitioning, covering and packing
• 05C45: Eulerian and Hamiltonian graphs
• 05C20: Directed graphs (digraphs), tournaments
• 05C38: Paths and cycles

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2012
• Tom: 32
• Numer: 2
• Strony: 357-372

Daty

wydano

2012

otrzymano

2010-10-06

poprawiono

2011-11-04

zaakceptowano

2011-11-14

Twórcy

autor

Mariusz Meszka

• AGH University of Science and Technology, Kraków, Poland

autor

Zdzisław Skupień

• AGH University of Science and Technology, Kraków, Poland

Bibliografia

• [1] C. Berge, Graphs and Hypergraphs (North-Holland, Amsterdam-London, 1973).
• [2] J.-C. Bermond and V. Faber, Decomposition of the complete directed graph into k-circuits, J. Combin. Theory (B) 21 (1976) 146-155, doi: 10.1016/0095-8956(76)90055-1.
• [3] J. Bosák, Decompositions of Graphs (Dordrecht, Kluwer, 1990).
• [4] G. Chartrand and L. Lesniak, Graphs and Digraphs (Chapman & Hall/CRC Boca Raton, 2004).
• [5] N.S. Mendelsohn, Hamiltonian decomposition of the complete directed n-graph, in: Theory of Graphs, Proc. Colloq., Tihany 1966, P. Erdös and G. Katona (Eds.), (Akadémiai Kiadó, Budapest, 1968) 237-241.
• [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.
• [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.
• [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.

Identyfikatory

DOI

10.7151/dmgt.1622