@article {
author = {Meng, Wei and Grueter, Steffen and Guo, Yubao and Kapolke, Manu and Meesker, Simon},
title = {t-Pancyclic Arcs in Tournaments},
journal = {Communications in Combinatorics and Optimization},
volume = {4},
number = {2},
pages = {123-130},
year = {2019},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2019.26333.1097},
abstract = {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 $t\leq \ell \leq |V(T)|$. 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 $3\leq t\leq |V(T)|$ and characterizing all tournaments which satisfy $h^t(T)= t$. We also present all tournaments which fulfill $p^t(T)= t$. },
keywords = {tournament,pancyclicity,t-pancyclic arc},
url = {http://comb-opt.azaruniv.ac.ir/article_13853.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_13853_b838a366c1fd609997bcb3c6948d3b01.pdf}
}