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t-pancyclic arcs in tournaments
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نویسنده
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meng wei ,grueter steffen ,guo yubao ,kapolke manu ,meesker simon
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منبع
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communications in combinatorics and optimization - 2019 - دوره : 4 - شماره : 2 - صفحه:123 -130
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چکیده
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Let t be a non-trivial tournament. an arc is emph{t-pancyclic} in t, if it is contained in a cycle of length ℓ for every t≤ℓ≤|v(t)|. let pt(t) denote the number of t-pancyclic arcs in t and ht(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 h3(t)≥3 for any non-trivial strong tournament t and characterized the tournaments with h3(t)=3. in this paper, we generalize moon's theorem by showing that ht(t)≥t for every 3≤t≤|v(t)| and characterizing all tournaments which satisfy ht(t)=t. we also present all tournaments which fulfill pt(t)=t.
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کلیدواژه
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tournament ,pancyclicity ,t-pancyclic arc
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آدرس
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shanxi university, school of mathematical sciences, china, rwth aachen university, germany, rwth aachen university, germany, rwth aachen university, germany, rwth aachen university, germany
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پست الکترونیکی
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simon.meesker@rwth-aachen.de
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Authors
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