A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most once. It is maximal 1-planar if the addition of any edge violates 1-planarity.Maximal 1-planar graphs have at most 4 n − 8 edges. We show that there are sparse maximal 1-planar ...
In this section, we want to describe some properties of doubly convex-bipartite graphs that will be used to construct a maximum biplanar subgraph. Suppose that G=(S,T,E) is a connected doubly convex-bipartite graph, and s1,s2,…,s|S| and t1,t2,…,t|T| are orderings of S and T,...
A graph is ISK4-free if it does not contain any induced subdivision of K4. Given a graph with large chromatic number, it is natural to ask whether it must contain induced subgraphs with particular properties. A family of graphs G is said to be χ-bounded if there exists a function f:...
Therefore, understanding how quantum and classical computing resources can be leveraged together is imperative for extracting maximal utility from quantum computers. An illustration of this hybrid scheme, in the context of this work, is shown in Fig. 1. In this work, we implement the variational ...
摘要: We prove the NP-completeness of a weighted version of the jump number problem on two-dimensional orders, by reducing the Maximum Independent Set on cubic planar graphs, using a geometrical construction.关键词:jump number dimension maximal independent set ...
Standard and newly designed building blocks for complex urban sites– also designated by urban archetypes - are used in this study to quantify the influence of urban forms on their energy demand and energy systems design. An energy hub, which consists on
Considering a RORI index alone, the best candidate response set is represented by a maximal positive RORI index. Therefore, the RORI index of a response plan yields a ranking of response plans for, e.g., an ongoing attack, while considering the cost of implementing and maintaining this respons...
Flow chemistry is the future of chemical processing. It represents a significant advance in energy consumption and waste generation regarding operations in batch and continuous flow macroscopic equipment since the transport rate (of mass, heat, photons, electrons, etc.) is tremendously intensified. In...
On empty convex polygons in a planar point set J. Comb. Theory, Ser. A, 113 (2006), pp. 385-419 Google Scholar [24] M. Sharir, A. Sheffer, E. Welzl Counting plane graphs: perfect matchings, spanning cycles, and Kasteleyn's technique J. Comb. Theory, Ser. A, 120 (2013), pp...
Aesthetics convert to restrictions if they are absolute, such as planar and straight line. Here we add unidirectional and shall consider upward planar graphs on the plane, the sphere, and the standing and the rolling cylinders. The task of drawing a graph consists of two phases: placement of ...