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

Title & Authors
THE NUMBER OF PANCYCLIC ARCS CONTAINED IN A HAMILTONIAN CYCLE OF A TOURNAMENT
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 $\small{3{\leq}l{\leq}n}$, 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 $\small{h(T){\geq}3}$ for all strong tournaments with $\small{n{\geq}3}$. Havet [4] later conjectured that $\small{h(T){\geq}2k+1}$ for all k-strong tournaments and proved the case k
Keywords
tournament;pancyclic arc;Hamiltonian cycle;
Language
English
Cited by
References
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