Cycles of given length in some K1,3-free graphs
نویسندگان
چکیده
منابع مشابه
Cycles 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 کاملEmbedding cycles of given length in oriented graphs
Kelly, Kühn and Osthus conjectured that for any ` ≥ 4 and the smallest number k ≥ 3 that does not divide `, any large enough oriented graph G with δ(G), δ−(G) ≥ b|V (G)|/kc+1 contains a directed cycle of length `. We prove this conjecture asymptotically for the case when ` is large enough compared to k and k ≥ 7. The case when k ≤ 6 was already settled asymptotically by Kelly, Kühn and Osthus.
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.
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Let ~ H be an orientation of a graph H. Alon and Yuster proposed the problem of determining or estimating D(n,m, ~ H), the maximum number of ~ H-free orientations a graph with n vertices and m edges may have. We consider the maximum number of ~ H-free orientations of typical graphs G(n,m) with n vertices and m edges. Suppose ~ H = C ` is the directed cycle of length ` > 3. We show that if m n 1...
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Let us write f(n, ∆; C2k+1) for the maximal number of edges in a graph of order n and maximum degree ∆ that contains no cycles of length 2k + 1. For n 2 ≤ ∆ ≤ n − k − 1 and n sufficiently large we show that f(n, ∆; C2k+1) = ∆(n −∆), with the unique extremal graph a complete
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1989
ISSN: 0012-365X
DOI: 10.1016/0012-365x(89)90186-6