%0 Journal Article
%T t-Pancyclic Arcs in Tournaments
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A Meng, Wei
%A Grueter, Steffen
%A Guo, Yubao
%A Kapolke, Manu
%A Meesker, Simon
%D 2019
%\ 12/01/2019
%V 4
%N 2
%P 123-130
%! t-Pancyclic Arcs in Tournaments
%K tournament
%K pancyclicity
%K t-pancyclic arc
%R 10.22049/cco.2019.26333.1097
%X Let $T$ be a non-trivial tournament. An arc is emph{$t$-pancyclic} in $T$, if it is contained in a cycle of length $ell$ for every $tleq ell leq |V(T)|$. Let $p^t(T)$ denote the number of $t$-pancyclic arcs in $T$ and $h^t(T)$ the maximum number of $t$-pancyclic arcs contained in the same Hamiltonian cycle of $T$. Moon ( J. Combin. Inform. System Sci., 19 (1994), 207-214) showed that $h^3(T)geq3$ for any non-trivial strong tournament $T$ and characterized the tournaments with $h^3(T)= 3$. In this paper, we generalize Moon's theorem by showing that $h^t(T)geq t$ for every $3leq tleq |V(T)|$ and characterizing all tournaments which satisfy $h^t(T)= t$. We also present all tournaments which fulfill $p^t(T)= t$.
%U http://comb-opt.azaruniv.ac.ir/article_13853_b838a366c1fd609997bcb3c6948d3b01.pdf