Monotone drawings of planar graphs Let G be a graph drawn in the plane so that its edges are represented by x -monotone curves, any pair of which cross an even number of times. We show that... J Pach,G Tóth - 《Journal of Graph Theory》 被引量: 79发表: 2004年 A lower bound on...
Graph theory is a branch of mathematics that studies the properties and relationships of graphs. A graph is a collection of nodes (also called vertices) and edges (also called branches) that connect the nodes. Graphs can be used to model many phenomena in science, engineering, and social scie...
In terms of graph theory this conjecture asserts that for every graph G with p = 9 points, either G or its complementary graph G is nonplanar. If this conjecture holds for graphs with 9 points, it clearly also holds for graphs with p > 9 points. It was remarked in the problem that ...
It is shown that embeddings of planar graphs in arbitrary surfaces other than the 2-sphere have a special structure. It turns out that these embeddings can be described in terms of noncontractible curves in the surface, meeting the graph in at most two points (which may taken to be ...
stereochemistry A0210 Algebra, set theory, and graph theoryIt is emphasized by means of counter-examples that the theorem of Gutman, Mallion and Essam (1983, Molec. Phys., 50, 859), for computing the number of spanning trees in a labelled graph, is generally valid only for planar graph...
Like past QAOA experiments, we study performance for problems defined on the planar connectivity graph native to our hardware; however, we also apply the QAOA to the Sherrington–Kirkpatrick model and MaxCut, non-native problems that require extensive compilation to implement. For hardware-native ...
1.non-planar condensed ring structure非平面密集环状结构 2.The graph K1 is hence nonplanar.于是,图K1是非平面的。 3.Graphic Non-Two Dimentional,The Application of the Visual Elements with the Multi-Dimensional Expression in Exhibition Space Design平面非平面——论平面视觉要素的多维化表述在展示空间中...
Included in the following conference series: Southeastern International Conference on Combinatorics, Graph Theory, and Computing 432 Accesses Abstract Let G be a graph with vertex set V(G) and edge set E(G). A (p, q)-graph G=(V,E) is said to be AL(k)-traversal if there exist a seq...
First, the contracted graphs of kinematic chains are classified according to their planarity, and all the planar-graph and non-planar-graph contracted graphs are generated. Then, synthesis constraint equations sets and simplified characteristic codes of topological graphs are provided, respectively. All ...
Thus, by defining planar layers in {s}, the model can be sliced with non-planar uniform layers parallel to the build platform. Commercial software was used to define these planar layers in {s}. To validate the methodology, two case studies have been defined and validated in a robotized ...