منابع مشابه
Unavoidable tournaments
A basic result in Ramsey theory states that any tournament contains a “large” transitive subgraph. Since transitive tournaments contain only transitive subgraphs, it is natural to ask which subgraphs must appear in any large tournament that is “far” from being transitive. One result of this type was obtained by Fox and Sudakov who characterized the tournaments that appear in any tournament that...
متن کاملTrees 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...
متن کاملUnavoidable trees and forests in graphs
Classic results from extremal graph theory state that if certain graphs are made large enough, unavoidable substructures appear. Here we will cover this type of problem for specific graphs when these substructures are certain trees or forests. After giving a summary on related results, the following two extremal main problems are presented: For a given family of same-order trees including the s...
متن کاملPaths, Trees and Cycles in Tournaments
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.
متن کاملOn k-ary spanning trees of tournaments
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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ژورنال
عنوان ژورنال: Random Structures & Algorithms
سال: 2018
ISSN: 1042-9832
DOI: 10.1002/rsa.20765