منابع مشابه
Boolean dimension and tree-width
The dimension of a partially ordered set P is an extensively studied parameter. Small dimension allows succinct encoding. Indeed if P has dimension d, then to know whether x < y in P it is enough to check whether x < y in each of the d linear extensions of a witnessing realizer. Focusing on the encoding aspect Nešetřil and Pudlák defined the boolean dimension so that P has boolean dimension at ...
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Over the last 30 years, researchers have investigated connections between dimension for posets and planarity for graphs. Here we extend this line of research to the structural graph theory parameter tree-width by proving that the dimension of a finite poset is bounded in terms of its height and the tree-width of its cover graph.
متن کاملBoolean Dimension and Local Dimension
Dimension is a standard and well-studied measure of complexity of posets. Recent research has provided many new upper bounds on the dimension for various structurally restricted classes of posets. Bounded dimension gives a succinct representation of the poset, admitting constant response time for queries of the form “is x < y?”. This application motivates looking for stronger notions of dimensi...
متن کاملBoolean-Width of Graphs
We introduce the graph parameter boolean-width, related to the number of different unions of neighborhoods across a cut of a graph. For many graph problems this number is the runtime bottleneck when using a divide-and-conquer approach. Boolean-width is similar to rank-width, which is related to the number of GF [2]-sums (1+1=0) of neighborhoods instead of the Boolean-sums (1+1=1) used for boole...
متن کاملHeight and Width of Superatomic Boolean Algebras
Cantor-Bendixson height and width of superatomic Boolean algebras is investigated and it is shown that (1) you don't need a Canadian tree to construct an u>,-thin-thick superatomic Boolean algebra; (2) c can be very large and for all k < c and all uncountable X, k < c, there are no K-thin-very tall, X-thin-tall, ic-very thin-thick, or X-thin-thick superatomic Boolean algebras on k. 0. Introduct...
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ژورنال
عنوان ژورنال: Combinatorica
سال: 2020
ISSN: 0209-9683,1439-6912
DOI: 10.1007/s00493-020-4000-9