On embeddability and stresses of graphs
نویسنده
چکیده
Gluck [6] has proven that triangulated 2-spheres are generically 3-rigid. Equivalently, planar graphs are generically 3-stress free. We show that already the K5-minor freeness guarantees the stress freeness. More generally, we prove that every Kr+2-minor free graph is generically r-stress free for 1 ≤ r ≤ 4. (This assertion is false for r ≥ 6.) Some further extensions are discussed.
منابع مشابه
Vertex Splitting and Upper Embeddable Graphs
The weak minor G of a graph G is the graph obtained from G by a sequence of edge-contraction operations on G. A weak-minor-closed family of upper embeddable graphs is a set G of upper embeddable graphs that for each graph G in G, every weak minor of G is also in G. Up to now, there are few results providing the necessary and sufficient conditions for characterizing upper embeddability of graphs...
متن کاملEmbeddability and Stresses of Graphs
Gluck [11] has proven that triangulated 2-spheres are generically 3-rigid. Equivalently, planar graphs are generically 3-stress free. We show that linklessly embeddable graphs are generically 4-stress free. Both of these results are corollaries of the following theorem: every Kr+2-minor free graph is generically r-stress free for 1 ≤ r ≤ 4. (This assertion is false for r ≥ 6.) We give an equiva...
متن کاملHigher-Degree Orthogonal Graph Drawing with Flexibility Constraints
Much work on orthogonal graph drawing has focused on 4-planar graphs, that is planar graphs where all vertices have maximum degree 4. In this work, we study aspects of the Kandinsky model, which is a model for orthogonal graph drawings of higher-degree graphs. First, we examine the decision problem β-Embeddability, which asks whether for a given planar graph with a fixed or variable embedding, ...
متن کاملOn computational complexity of length embeddability of graphs
A graph G is embeddable in Rd if vertices of G can be assigned with points of Rd in such a way that all pairs of adjacent vertices are at the distance 1. We show that verifying embeddability of a given graph in Rd is NP-hard in the case d > 2 for all reasonable notions of embeddability.
متن کاملManhattan-Geodesic Embedding of Planar Graphs
In this paper, we explore a new convention for drawing graphs, the (Manhattan-) geodesic drawing convention. It requires that edges are drawn as interior-disjoint monotone chains of axis-parallel line segments, that is, as geodesics with respect to the Manhattan metric. First, we show that geodesic embeddability on the grid is equivalent to 1-bend embeddability on the grid. For the latter quest...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Combinatorica
دوره 27 شماره
صفحات -
تاریخ انتشار 2007