On Subtrees of Directed Graphs with No Path of Length Exceeding One
1970 ◽
Vol 13
(3)
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pp. 329-332
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The following theorem was conjectured to hold by P. Erdös [1]:Theorem 1. For each finite directed tree T with no directed path of length 2, there exists a constant c(T) such that if G is any directed graph with n vertices and at least c(T)n edges and n is sufficiently large, then T is a subgraph of G. In this note we give a proof of this conjecture. In order to prove Theorem 1, we first need to establish the following weaker result.
1982 ◽
Vol 25
(1)
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pp. 119-120
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1975 ◽
Vol 27
(2)
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pp. 348-351
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Keyword(s):
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2015 ◽
Vol 24
(6)
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pp. 873-928
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2015 ◽
Vol 49
(6)
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pp. 221-231
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2017 ◽
Vol 27
(03)
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pp. 207-219