Some Results on Disk Graphs

陳哲烱中國科技大學 (台灣 )

Joint work with 李國偉、林瑩貞

OUTLINE

• Basic Definition

• Examples and Forbidden Subgraphs of CD Graphs

• Examples of UD Graphs

• Forbidden Subgraphs of UD Graphs

Basic Definition

Disk graphs are motivated to model radio broadcast

networks and cellular telephone networks. We usually

model these networks by an interfere graph with

vertices representing transmitters. And two vertices

are adjacent if the signals of transmitters interfere.

Intersection Disk

(ID)

A B

A B

Unit Disk

(UD)

Containment Disk

(CD)

A B A B

Basic Definition

Basic Definition

Basic Definition

Examples and Forbidden Subgraphs of CD Graphs

Examples of UD Graphs

Forbidden Subgraphs of UD Graphs

Forbidden Subgraphs of UD Graphs

Forbidden Subgraphs of UD Graphs

Conditions for cases to be UD and CD graphs

Some Forbidden Subgraphs of UD Graphs

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