A well-quasi-order for tournaments
نویسندگان
چکیده
A digraph H is immersed in a digraph G if the vertices of H are mapped to (distinct) vertices of G, and the edges of H are mapped to directed paths joining the corresponding pairs of vertices of G, in such a way that the paths are pairwise edge-disjoint. For graphs the same relation (using paths instead of directed paths) is a well-quasi-order; that is, in every infinite set of graphs some one of them is immersed in some other. The same is not true for digraphs in general; but we show it is true for tournaments (a tournament is a directed complete graph).
منابع مشابه
Tournaments that omit N 5 are well - quasi - ordered by Brenda
The tournament N5 can be obtained from the transitive tournament on {1, . . . , 5}, with the natural order, by reversing the edges between successive vertices. Tournaments that do not have N5 as a subtournament are said to omit N5. We describe the structure of tournaments that omit N5 and use this with Kruskal’s Tree Theorem to prove that this class of tournaments is well-quasi-ordered. The pro...
متن کاملStrong immersion is a well-quasi-ordering for semi-complete digraphs
We prove that the strong immersion order is a well-quasi-ordering on the class of semi-complete digraphs, thereby strengthening a result of Chudnovsky and Seymour [2] that this holds for the class of tournaments.
متن کاملColoring tournaments with forbidden substructures
Coloring graphs is an important algorithmic problem in combinatorics with many applications in computer science. In this paper we study coloring tournaments. A chromatic number of a random tournament is of order Ω( n log(n)). The question arises whether the chromatic number can be proven to be smaller for more structured nontrivial classes of tournaments. We analyze the class of tournaments def...
متن کاملTournament minors
We say a digraph G is a minor of a digraph H if G can be obtained from a subdigraph of H by repeatedly contracting a strongly-connected subdigraph to a vertex. Here, we show the class of all tournaments is a well-quasi-order under minor containment.
متن کاملA classification of arc-locally semicomplete digraphs
Tournaments are without doubt the best studied class of directed graphs [3, 6]. The generalizations of tournaments arise in order to extend the well-known results on tournaments to more general classes of directed graphs. Moreover, the knowledge about generalizations of tournaments has allowed to deepen our understanding of tournaments themselves. The semicomplete digraphs, the semicomplete mul...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 101 شماره
صفحات -
تاریخ انتشار 2011