منابع مشابه
Adjacency posets of planar graphs
In this paper, we show that the dimension of the adjacency poset of a planar graph is at most 8. From below, we show that there is a planar graph whose adjacency poset has dimension 5. We then show that the dimension of the adjacency poset of an outerplanar graph is at most 5. From below, we show that there is an outerplanar graph whose adjacency poset has dimension 4. We also show that the dim...
متن کاملPosets and planar graphs
Usually dimension should be an integer valued parameter. We introduce a refined version of dimension for graphs, which can assume a value 1⁄2 t 1l t , thought to be between t 1 and t. We have the following two results: (a) a graph is outerplanar if and only if its dimension is at most 1⁄22l3 . This characterization of outerplanar graphs is closely related to the celebrated result of W. Schnyder...
متن کاملSegmenting Planar Superpixel Adjacency Graphs w.r.t. Non-planar Superpixel Affinity Graphs
We address the problem of segmenting an image into a previously unknown number of segments from the perspective of graph partitioning. Specifically, we consider minimum multicuts of superpixel affinity graphs in which all affinities between non-adjacent superpixels are negative. We propose a relaxation by Lagrangian decomposition and a constrained set of re-parameterizations for which we can op...
متن کاملThe Dimension of Posets with Planar Cover Graphs
Kelly showed that there exist planar posets of arbitrarily large dimension, and Streib and Trotter showed that the dimension of a poset with a planar cover graph is bounded in terms of its height. Here we continue the study of conditions that bound the dimension of posets with planar cover graphs. We show that if P is a poset with a planar comparability graph, then the dimension of P is at most...
متن کاملPlanar multi-patch domain parameterization via patch adjacency graphs
As a remarkable difference to the existing CAD technology, where shapes are represented by their boundaries, FEM-based isogeometric analysis typically needs a parameterization of the interior of the domain. Due to the strong influence on the accuracy of the analysis, methods for constructing a good parameterization are fundamentally important. The flexibility of single patch representations is ...
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: 2010
ISSN: 0012-365X
DOI: 10.1016/j.disc.2009.11.005