Trees in tournaments
نویسندگان
چکیده
منابع مشابه
Trees in tournaments
A digraph is said to be n-unavoidable if every tournament of order n contains it as a subgraph. Let f (n) be the smallest integer such that every oriented tree is f (n)-unavoidable. Sumner (see 7]) noted that f (n) 2n ? 2 and conjetured that equality holds. HH aggkvist and Thomason established the upper bounds f (n) 12n and f (n) (4 + o(1))n. Let g(k) be the smallest integer such that every ori...
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We survey results on paths, trees and cycles in tournaments. The main subjects are hamiltonian paths and cycles, vertex and arc disjoint paths with prescribed endvertices, arc-pancyclicity, oriented paths, trees and cycles in tournaments. Several unsolved problems are included.
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It is well known that every tournament contains a Hamiltonian path, which can be restated as that every tournament contains a unary spanning tree. The purpose of this article is to study the general problem of whether a tournament contains a k-ary spanning tree. In particular, we prove that, for any fixed positive integer k, there exists a minimum number h(k) such that every tournament of order...
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متن کاملt-Pancyclic Arcs in Tournaments
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 $tleq ell leq |V(T)|$. 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 ({em J. Combin. Inform. System Sci.}, {bf 19} (1994), 207-214) showed that $...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2002
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(00)00463-5