A Classification of Antichains of Finite Tournaments
نویسنده
چکیده
Tournament embedding is an order relation on the class of finite tournaments. An antichain is a set of finite tournaments that are pairwise incomparable in this ordering. We say an antichain A can be extended to an antichain B if A ⊆ B. Those finite antichains that can not be extended to antichains of arbitrarily large finite cardinality are exactly those that contain a member of each of four families of tournaments. We give an upper bound on the cardinality of extensions of such antichains. This bound depends on the maximum order of the tournaments in the antichain.
منابع مشابه
On Blockers in Bounded Posets
Antichains of a finite bounded poset are assigned antichains playing a role analogous to that played by blockers in the Boolean lattice of all subsets of a finite set. Some properties of lattices of generalized blockers are discussed. 2000 Mathematics Subject Classification. 06A06, 90C27.
متن کاملEmbedded antichains in tournaments
The maximum antichain cardinality (MACC) of a tournament is the maximum number of incomparable subtournaments of T . We establish some properties of MACC. We describe all tournaments whose MACC is 1 or 2, show that MACC can grow exponentially with the size of the vertex set of a tournament, and present some questions for further investigation.
متن کاملOn canonical antichains
An antichain A of a well-founded quasi-order (E,≤) is canonical if for every finite subset A0 of A, all antichains of E\{x : x ≥ a for some a in A\A0} are finite. In this paper, we characterize those quasi-orders that have a canonical antichain. Guoli Ding, On canonical antichains, (July 20, 1994) 1
متن کاملSplitting finite antichains in the homomorphism order
A structural condition is given for finite maximal antichains in the homomorphism order of relational structures to have the splitting property. It turns out that non-splitting antichains appear only at the bottom of the order. Moreover, we examine looseness and finite antichain extension property for some subclasses of the homomorphism poset. Finally, we take a look at cut-points in this order.
متن کاملOn Finite Maximal Antichains in the Homomorphism Order
The relation of existence of a homomorphism on the class of all relational structures of a fixed type is reflexive and transitive; it is a quasiorder. There are standard ways to transform a quasiorder into a partial order – by identifying equivalent objects, or by choosing a particular representative for each equivalence class. The resulting partial order is identical in both cases. Properties ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2002