Geometric intersection graphs
WebOct 15, 2024 · Our interest lies in geometric intersection graphs, where the nodes correspond to geometric objects and there is an arc between two nodes iff the corresponding objects intersect. If the objects are disks, the resulting graph is called a disk graph. Disk graphs, and in particular unit-disk graphs, are a popular model for wireless … WebFeb 20, 2024 · Graph \(G'\) is the intersection graph of 2n geometric objects S, where each object has occurred twice in the same position. Clearly, the number of vertices and edges in \(G'\) are polynomial in the number of vertices of G ; hence, the construction can be done in polynomial time.
Geometric intersection graphs
Did you know?
WebSep 9, 2024 · We study the computational complexity landscape of the BCS problem while considering geometric intersection graphs. On one hand, we prove that the BCS problem is NP-hard on the unit disk, outer ... WebJul 27, 2006 · A disk graph is the intersection graph of a set of disks with arbitrary diameters in the plane. For the case that the disk representation is given, we present …
WebSep 11, 2024 · 1. Introduction. The of a collection of sets is a graph where each vertex of the graph represents a set, and there is an edge between two vertices if their … WebSep 11, 2024 · 1. Introduction. The of a collection of sets is a graph where each vertex of the graph represents a set, and there is an edge between two vertices if their corresponding sets intersect. Note that any graph can be represented as an intersection graph over some sets. Geometric intersection graph families consist of intersection graphs for …
WebMar 1, 2024 · Two paths from s to t are (interior-)vertex-disjoint if their only common vertices are s and t. By Menger's theorem (see, for example, [26, Section 8.2] ), the minimum … Many important graph families can be described as intersection graphs of more restricted types of set families, for instance sets derived from some kind of geometric configuration: An interval graph is defined as the intersection graph of intervals on the real line, or of connected subgraphs of a … See more In graph theory, an intersection graph is a graph that represents the pattern of intersections of a family of sets. Any graph can be represented as an intersection graph, but some important special classes of graphs can be … See more Any undirected graph G may be represented as an intersection graph. For each vertex vi of G, form a set Si consisting of the … See more • Contact graph See more • Jan Kratochvíl, A video lecture on intersection graphs (June 2007) • E. Prisner, A Journey through Intersection Graph County See more Formally, an intersection graph G is an undirected graph formed from a family of sets $${\displaystyle S_{i},\,\,\,i=0,1,2,\dots }$$ by creating one vertex vi for each set Si, and connecting two vertices vi and vj by an edge whenever … See more An order-theoretic analog to the intersection graphs are the inclusion orders. In the same way that an intersection representation of a … See more • For an overview of both the theory of intersection graphs and important special classes of intersection graphs, see McKee & McMorris (1999). See more
WebIn this paper, we focus on geometric intersection graphs of objects in the plane only. Because Feedback Vertex Set onunitballgraphsin R 3 hasnosubexponential-time algorithmparameterizedby k unlessETHfails[16]. bar turbineWebproximation algorithms for problems on unit disk graphs and other geometric intersection graphs. The method is based on approximating the input set of geometric objects, which can be arbitrarily dense, by a sparse set of objects, that is, a set of objects such that any square of constant size contains at most a constant number of objects. bar t urbanaWebAug 29, 2013 · A graph is triangle-free if it contains no clique of size 3. It is clear that \chi (G)\geqslant \omega (G). On the one hand, the chromatic and clique numbers of a graph … sve igrice pucanjeWebHere we study the conflict-free coloring of geometric intersection graphs. We demonstrate that the intersection graph of n geometric objects without fatness properties and size restrictions may have conflict-free chromatic number in Ω (log n / log log n) and in Ω (log n) for disks or squares of different sizes; it is known for general graphs ... bar turbigoWebproved for intersection graphs of continuous curves, each intersecting the x-axis in precisely one point. Due to space limitations and personal preferences, many classical … sve igre sa kartamaWebPlanar Graph; Intersection Graph; Geometric Graph; Polynomial Time Approximation Scheme; Frequency Assignment; These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves. sve igreIn computer science, several computational problems related to independent sets have been studied. • In the maximum independent set problem, the input is an undirected graph, and the output is a maximum independent set in the graph. If there are multiple maximum independent sets, only one need be output. This problem is sometimes referred to as "vertex packing". sve igrice poki