Study of Disk Graph

• Main Authors: Ying-Jen Lin, 林瑩貞
• Other Authors: Ko-Wei Lih
• Format: Others
• Language: en_US
• Published: 2000
• Online Access: http://ndltd.ncl.edu.tw/handle/88073775230136736668

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.