منابع مشابه
Tree-Width and Dimension
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 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 ...
متن کاملThe 2-dimension of a Tree
Let $x$ and $y$ be two distinct vertices in a connected graph $G$. The $x,y$-location of a vertex $w$ is the ordered pair of distances from $w$ to $x$ and $y$, that is, the ordered pair $(d(x,w), d(y,w))$. A set of vertices $W$ in $G$ is $x,y$-located if any two vertices in $W$ have distinct $x,y$-location.A set $W$ of vertices in $G$ is 2-located if it is $x,y$-located, for some distinct...
متن کاملTree-width and planar minors
Robertson and the second author [7] proved in 1986 that for all h there exists f(h) such that for every h-vertex simple planar graph H, every graph with no H-minor has tree-width at most f(h); but how small can we make f(h)? The original bound was an iterated exponential tower, but in 1994 with Thomas [9] it was improved to 2O(h 5); and in 1999 Diestel, Gorbunov, Jensen, and Thomassen [3] prove...
متن کاملBounding connected tree-width
Diestel and Müller showed that the connected tree-width of a graph G, i. e., the minimum width of any tree-decomposition with connected parts, can be bounded in terms of the tree-width of G and the largest length of a geodesic cycle in G. We improve their bound to one that is of correct order of magnitude. Finally, we construct a graph whose connected tree-width exceeds the connected order of a...
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ژورنال
عنوان ژورنال: Combinatorica
سال: 2015
ISSN: 0209-9683,1439-6912
DOI: 10.1007/s00493-014-3081-8