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GraphTheory

  

IntervalGraph

  

construct an interval graph

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

IntervalGraph( c )

Parameters

c

-

a list, Vector, or 1-D Array of intervals

Description

• 

The IntervalGraph( c ) command returns an interval graph for the collection of intervals c.

• 

Each element of the input c must be a range or a RealRange expression. A range a..b is interpreted as the closed real interval from a to b. To specify open or half-open intervals, you can use RealRange.

• 

An interval graph is the intersection graph of a set of intervals on the real line. For any vertices i, j in the the graph, an edge between i and j exists if and only if the intervals i and j intersect.

Examples

Compute the interval graph for {1..3, 2..4, 3..5}.

withGraphTheory:

GIntervalGraph1..3,2..4,3..5

GGraph 1: an undirected unweighted graph with 3 vertices and 3 edge(s)

(1)

Construct a schedule to distribute a set of business meetings across several conference rooms.

Meetings9..11.5,9.5..10,9.75..15,11.5..15,12.5..13.5,14.5..17,16.5..17.5

Meetings9..11.5,9.5..10,9.75..15,11.5..15,12.5..13.5,14.5..17,16.5..17.5

(2)

RoomNamesSuite Infinity,Geddes Suite,Taylor's Suite

RoomNamesSuite Infinity,Geddes Suite,Taylor's Suite

(3)

ScheduleGreedyColorIntervalGraphMeetings

Schedule3,1,2,0,2,1,1,0

(4)

RoomiRoomNamesSchedule2ListTools:−Searchi,Meetings+1:

ListTools:-ClassifyRoom,Meetings

tableSuite Infinity=9.75..15,16.5..17.5,Taylor's Suite=9.5..10,11.5..15,Geddes Suite=9..11.5,12.5..13.5,14.5..17

(5)

The following interval graph has only edge because the intervals 0..1 and 1..2 intersect at 1, but the half-open interval −1,0 does not intersect 0..1.

IntervalGraph( [ RealRange(-1,Open(0)), 0..1, 1..2 ] );

Visualize the relationships within a set of intervals.

GIntervalGraph0..8,1..π,exp1..20,7..18,11..14,RealRange17,Open23,23..25

GGraph 2: an undirected unweighted graph with 7 vertices and 9 edge(s)

(6)

DrawGraphG

Compatibility

• 

The GraphTheory[IntervalGraph] command was introduced in Maple 2016.

• 

For more information on Maple 2016 changes, see Updates in Maple 2016.

• 

The GraphTheory[IntervalGraph] command was updated in Maple 2020.

See Also

GraphTheory