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THE NUMBER OF PANCYCLIC ARCS CONTAINED IN A HAMILTONIAN CYCLE OF A TOURNAMENT
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 Title & Authors
THE NUMBER OF PANCYCLIC ARCS CONTAINED IN A HAMILTONIAN CYCLE OF A TOURNAMENT
Surmacs, Michel;
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 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
 Cited by
 References
1.
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.
F. Havet, Pancyclic arcs and connectivity in tournaments, J. Graph Theory 47 (2004), no. 2, 87-110. crossref(new window)

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.

6.
C. Thomassen, Hamiltonian-connected tournaments, J. Combin. Theory Ser. B 28 (1980), no. 2, 142-163. crossref(new window)

7.
A. Yeo, The number of pancyclic arcs in a k-strong tournament, J. Graph Theory 50 (2005), no. 3, 212-219. crossref(new window)