Meager-nowhere dense games (VI): Markov $k$-tactics
نویسندگان
چکیده
منابع مشابه
Meager-nowhere Dense Games (iii): Remainder Strategies
Player ONE chooses a meager set and player TWO, a nowhere dense set per inning. They play ω many innings. ONE's consecutive choices must form a (weakly) increasing sequence. TWO wins if the union of the chosen nowhere dense sets covers the union of the chosen meager sets. A strategy of TWO which depends on knowing only the uncovered part of the most recently chosen meager set is said to be a re...
متن کاملOn nowhere dense graphs
A set A of vertices of a graph G is called d-scattered in G if no two d-neighborhoods of (distinct) vertices of A intersect. In other words, A is d-scattered if no two distinct vertices of A have distance at most 2d. This notion was isolated in the context of finite model theory by Gurevich and recently it played a prominent role in the study of homomorphism preservation theorems for special cl...
متن کاملCharacterisations of Nowhere Dense Graphs
Nowhere dense classes of graphs were introduced by Nešetřil and Ossona de Mendez as a model for “sparsity” in graphs. It turns out that nowhere dense classes of graphs can be characterised in many different ways and have been shown to be equivalent to other concepts studied in areas such as (finite) model theory. Therefore, the concept of nowhere density seems to capture a natural property of g...
متن کاملCovering games and the Banach-Mazur game: k-tactics
Given a free ideal J of subsets of a set X, we consider games where player ONE plays an increasing sequence of elements of the σ-completion of J , and player TWO tries to cover the union of this sequence by playing one set at a time from J . We describe various conditions under which player TWO has a winning strategy that uses only information about the most recent k moves of ONE, and apply som...
متن کاملOn nowhere dense and somewhere dense - a graph trichotomy
Motivated by structural decompositions and other asymptotic properties of graphs we define the notions in the title and show the wide spectrum of examples of nowhere dense graphs. This has several algorithmic consequences and it generalizes and improves earlier results.
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: Illinois Journal of Mathematics
سال: 1996
ISSN: 0019-2082
DOI: 10.1215/ijm/1255986098