![]() ![]() Dominating sets in unit disk graphs are widely studied due to their application in wireless ad-hoc networks. Unbounded from Monopolarity assuming Polynomial,NP-complete disjoint. A unit disk graph is the intersection graph of n congruent disks in the plane. Its distance to clique is the minimum number of vertices that have to be deleted from $G$ in order to obtain a clique. UDGs are the intersection graphs of disks of unit radius (called unit disks) in the plane. Unbounded from Weighted independent set assuming Polynomial,NP-complete disjoint. Unbounded from Weighted independent dominating set assuming Polynomial,NP-complete disjoint. Unbounded from Weighted feedback vertex set assuming Polynomial,NP-complete disjoint. Unbounded from Polarity assuming Polynomial,NP-complete disjoint. Unbounded from Maximum cut assuming Polynomial,NP-complete disjoint. Unbounded from Independent set assuming Polynomial,NP-complete disjoint. None of the papers answer whether the following problem is NP-hard: Given a unit disk graph G ( V, E), find a configuration of a set D of. I have looked up several references 2 3 4. However, the paper does not mention how hard the realization problem is. Unbounded from Hamiltonian path assuming Polynomial,NP-complete disjoint. It is known that recognizing a unit disk graph is NP-hard 1. Unbounded from Hamiltonian cycle assuming Polynomial,NP-complete disjoint. Unbounded from Feedback vertex set assuming Polynomial,NP-complete disjoint. This is a nice example where reconstruction could be motivated by some optimization problem. Nevertheless it turns out that a maximum clique can be found in polynomial time provided we have the model available. Unbounded from Domination assuming Polynomial,NP-complete disjoint. Every generalized octhedron O is a unit-disk graph. Unbounded from Colourability assuming Polynomial,NP-complete disjoint. Unbounded from Clique cover assuming Polynomial,NP-complete disjoint. Unbounded from 3-Colourability assuming Polynomial,NP-complete disjoint. Is a bijection from $V(G)$ to the leaves of the tree $T$. Consider the following decomposition of a graph $G$ which is defined as a pair $(T,L)$ where $T$ is a binary tree and $L$ Matsui, Tomomi (2000), "Approximation Algorithms for Maximum Independent Set Problems and Fractional Coloring Problems on Unit Disk Graphs", Lecture Notes in Computer Science, Lecture Notes in Computer Science 1763: 194–200, doi: 10.1007/978-5-7_16, ISBN 978-1-7.(1994), Geometry based heuristics for unit disk graphs. Müller, Tobias (2011), "Sphere and dot product representations of graphs", Proceedings of the Twenty-Seventh Annual Symposium on Computational Geometry (SoCG'11), June 13–15, 2011, Paris, France, pp. 308–314. An example of a graph that is not a unit disk graph is the star \displaystyle-free graphs", Discrete Applied Mathematics 284: 53–60, doi: 10.1016/j.dam.2020.03.024 Unit disk graphs may be formed in a different way from a collection of equal-radius circles, by connecting two circles with an edge whenever one circle contains the center of the other circle.Įvery induced subgraph of a unit disk graph is also a unit disk graph.These graphs have a vertex for each circle or disk, and an edge connecting each pair of circles or disks that have a nonempty intersection. Unit disk graphs are the intersection graphs of equal-radius circles, or of equal-radius disks.Unit disk graphs are the graph formed from a collection of points in the Euclidean plane, with a vertex for each point and an edge connecting each pair of points whose distance is below a fixed threshold.There are several possible definitions of the unit disk graph, equivalent to each other up to a choice of scale factor: ![]()
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