Cycles of a given length in tournaments
نویسندگان
چکیده
We study the asymptotic behavior of maximum number directed cycles a given length in tournament: let c(ℓ) be limit ratio ℓ an n-vertex tournament and expected random tournament, when n tends to infinity. It is well-known that c(3)=1 c(4)=4/3. show c(ℓ)=1 if only not divisible by four, which settles conjecture Bartley Day. If we 1+2⋅(2/π)ℓ≤c(ℓ)≤1+(2/π+o(1))ℓ determine value exactly for ℓ=8. also give full description structure tournaments with four or ℓ∈{4,8}.
منابع مشابه
Cycles through a given arc in almost regular multipartite tournaments
If x is a vertex of a digraph D, then we denote by d(x) and d−(x) the outdegree and the indegree of x, respectively. The global irregularity of a digraph D is defined by ig(D) = max{d+(x), d−(x)}−min{d+(y), d−(y)} over all vertices x and y of D (including x = y). If ig(D) = 0, then D is regular and if ig(D) ≤ 1, then D is almost regular. A c-partite tournament is an orientation of a complete c-...
متن کاملOn Cycles Containing a Given Arc in Regular Multipartite Tournaments
In this paper we prove that if T is a regular n-partite tournament with n ≥ 4, then each arc of T lies on a cycle whose vertices are from exactly k partite sets for k = 4, 5, . . . , n. Our result, in a sense, generalizes a theorem due to Alspach.
متن کاملCycles Containing a Given Arc in Regular Multipartite Tournaments
In this paper we prove that if T is a regular n-partite tournament with n≥6, then each arc of T lies on a k-cycle for k=4,5,···,n. Our result generalizes theorems due to Alspach and Guo respectively.
متن کاملCycles of given length in oriented graphs
The Caccetta-Häggkvist conjecture would determine the minimum outdegree which forces a cycle of length at most k in an oriented graph. We study the related question of which minimum outand indegree forces a cycle of length exactly k in an oriented graph. We answer this question whenever k is not a multiple of 3 and propose a conjecture for the other cases.
متن کاملAlmost Given Length Cycles in Digraphs
A digraph is called k-cyclic if it cannot be made acyclic by removing less than k arcs. It is proved that for every > 0 there are constants K and δ so that for every d ∈ (0, δn), every n2-cyclic digraph with n vertices contains a directed cycle whose length is between d and d+K. A more general result of the same form is obtained for blow-ups of directed cycles.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2023
ISSN: ['0095-8956', '1096-0902']
DOI: https://doi.org/10.1016/j.jctb.2022.07.007