THE NUMBER OF PANCYCLIC ARCS CONTAINED IN A HAMILTONIAN CYCLE OF A TOURNAMENT

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 51, Issue 6, 2014, pp.1649-1654
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2014.51.6.1649

Title & Authors

THE NUMBER OF PANCYCLIC ARCS CONTAINED IN A HAMILTONIAN CYCLE OF A TOURNAMENT

Surmacs, Michel;

Surmacs, Michel;

Abstract

A tournament T is an orientation of a complete graph and an arc in T is called pancyclic if it is contained in a cycle of length l for all , where n is the cardinality of the vertex set of T. In 1994, Moon [5] introduced the graph parameter h(T) as the maximum number of pancyclic arcs contained in the same Hamiltonian cycle of T and showed that for all strong tournaments with . Havet [4] later conjectured that for all k-strong tournaments and proved the case k = 2. In 2005, Yeo [7] gave the lower bound for all k-strong tournaments T. In this note, we will improve his bound to .

Keywords

tournament;pancyclic arc;Hamiltonian cycle;

Language

English

References

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J. Bang-Jensen and G. Gutin, Digraphs: Theory, Algorithms and Applications, Springer, London, 2000.

2.

P. Camion, Chemins et circuits hamiltoniens des graphes complets, C. R. Acad. Sci. Paris 249 (1959), 2151-2152.

3.

J. Feng, Hamiltonian Cycles in Certain Graphs and Out-arc Pancyclic Vertices in Tournaments, Ph.D. thesis, 67-68, RWTH Aachen, 2008.

4.

5.

J. W. Moon, On k-cyclic and pancyclic arcs in strong tournaments, J. Combin. Inform. System Sci. 19 (1994), no. 3-4, 207-214.