Interval dimension is a comparability invariant
نویسندگان
چکیده
منابع مشابه
The Dimension of a Comparability Graph
Dushnik and Miller defined the dimension of a partial order P as the minimum number of linear orders whose intersection is P. Ken Bogart asked if the dimension of a partial order is an invariant of the associated comparability graph. In this paper we answer Bogart's question in the affirmative. The proof involves a characterization of the class of comparability graphs defined by Aigner and Prin...
متن کاملInterval orders and dimension
We show that for every interval order X , there exists an integer t so that if Y is any interval order with dimension at least t, then Y contains a subposet isomorphic to X .
متن کاملDimension and Matchings in Comparability and Incomparability Graphs
We develop some new inequalities for the dimension of a finite poset. These inequalities are then used to bound dimension in terms of the maximum size of matchings. We prove that if the dimension of P is d and d ≥ 3, then there is a matching of size d in the comparability graph of P . There is no analogue of this result for cover graphs, as we show that there is a poset P of dimension d for whi...
متن کاملFractal dimension of a random invariant set
In recent years many deterministic parabolic equations have been shown to possess global attractors which, despite being subsets of an infinite-dimensional phase space, are finite-dimensional objects. Debussche showed how to generalize the deterministic theory to show that the random attractors of the corresponding stochastic equations have finite Hausdorff dimension. However, to deduce a param...
متن کاملThe Fractal Dimension of Invariant Subsets for Piecewise Monotonic Maps on the Interval
We consider completely invariant subsets A of weakly expanding piecewise monotonic transformations T on [0, 1]. It is shown that the upper box dimension of A is bounded by the minimum tA of all parameters t for which a t-conformal measure with support A exists. In particular, this implies equality of box dimension and Hausdorff dimension of A.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1991
ISSN: 0012-365X
DOI: 10.1016/0012-365x(91)90010-y