| Summary: | 碩士 === 國立臺灣大學 === 數學研究所 === 88 === Study of Disk Graphs
Student: Ying-Jen Lin
Advisor: Dr. Ko-Wei Lih
Department of Mathematics
National Taiwan University
Abstract
Disk graphs are motivated to model radio broadcast networks [11] and cellular telephone networks. We usually model these networks by an interference graph with vertices representing transmitters and disks representing their transmitting ranges. And two vertices are adjacent if the signals of transmitters interfere. The problem of assigning distinct frequencies for transmitters with intersecting range corresponds to the minimum coloring problem for disk graphs.
Unit disk (UD) graphs, intersection disk (ID) graphs and constrained intersection disk (CID) graphs are the intersection graphs of disks with unit, arbitrary and constrained different radii in the plane, respectively. Constrained coin (CCOIN) graphs are the contact graphs of disks with constrained different radii in the plane. Containment disk (CD) graphs are the graphs of disks in which one contains the center of another with arbitrary radii in the plane.
The recognition problems for UD[3], ID[14] graphs are NP-hard. We find some forbidden subgraphs and examples for UD, ID and CD graphs in this study.
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