Traffic Lights, Graph Theory Problems…
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Now, for starters, I feel that this picture must be represented Graphically and the solution does show a Graph, which is given below
s 
But I am unable to understand this explanation. Could someone please explain this by perhaps giving an example?
Edit:
What is the equivalent graph of this figure?
graph-theory
asked May 31 '17 at 14:59
Hello_World
3,37821429
add a comment |Â
up vote
1
down vote
favorite
Now, for starters, I feel that this picture must be represented Graphically and the solution does show a Graph, which is given below
s
But I am unable to understand this explanation. Could someone please explain this by perhaps giving an example?
Edit:
What is the equivalent graph of this figure?
graph-theory
asked May 31 '17 at 14:59
Hello_World
3,37821429
What part of the explanation is unclear to you? The more specific you are, the more likely it is you'll get the clarification you seek.
– Fabio Somenzi
May 31 '17 at 15:19
I would like to know how the graph is built....
– Hello_World
May 31 '17 at 15:55
That isn't very specific, is it? Have you read the answer by @Evargalo?
– Fabio Somenzi
May 31 '17 at 15:59
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Now, for starters, I feel that this picture must be represented Graphically and the solution does show a Graph, which is given below
s
But I am unable to understand this explanation. Could someone please explain this by perhaps giving an example?
Edit:
What is the equivalent graph of this figure?
graph-theory
asked May 31 '17 at 14:59
Hello_World
3,37821429
Now, for starters, I feel that this picture must be represented Graphically and the solution does show a Graph, which is given below
s
But I am unable to understand this explanation. Could someone please explain this by perhaps giving an example?
Edit:
What is the equivalent graph of this figure?
graph-theory
graph-theory
asked May 31 '17 at 14:59
Hello_World
3,37821429
asked May 31 '17 at 14:59
Hello_World
3,37821429
edited May 31 '17 at 17:05
asked May 31 '17 at 14:59
Hello_World
3,37821429
asked May 31 '17 at 14:59
Hello_World
3,37821429
asked May 31 '17 at 14:59
Hello_World
3,37821429
3,37821429
What part of the explanation is unclear to you? The more specific you are, the more likely it is you'll get the clarification you seek.
– Fabio Somenzi
May 31 '17 at 15:19
I would like to know how the graph is built....
– Hello_World
May 31 '17 at 15:55
That isn't very specific, is it? Have you read the answer by @Evargalo?
– Fabio Somenzi
May 31 '17 at 15:59
add a comment |Â
What part of the explanation is unclear to you? The more specific you are, the more likely it is you'll get the clarification you seek.
– Fabio Somenzi
May 31 '17 at 15:19
I would like to know how the graph is built....
– Hello_World
May 31 '17 at 15:55
That isn't very specific, is it? Have you read the answer by @Evargalo?
– Fabio Somenzi
May 31 '17 at 15:59
What part of the explanation is unclear to you? The more specific you are, the more likely it is you'll get the clarification you seek.
– Fabio Somenzi
May 31 '17 at 15:19
What part of the explanation is unclear to you? The more specific you are, the more likely it is you'll get the clarification you seek.
– Fabio Somenzi
May 31 '17 at 15:19
I would like to know how the graph is built....
– Hello_World
May 31 '17 at 15:55
I would like to know how the graph is built....
– Hello_World
May 31 '17 at 15:55
That isn't very specific, is it? Have you read the answer by @Evargalo?
– Fabio Somenzi
May 31 '17 at 15:59
That isn't very specific, is it? Have you read the answer by @Evargalo?
– Fabio Somenzi
May 31 '17 at 15:59
add a comment |Â
2 Answers
2
active
oldest
votes
up vote
1
down vote
accepted
Answering the edit:
In the graph associated to your second example of intersection:
It has 8 vertices (L1 to L8)
Its edges are:
(listing only the links that have not already been mentioned)
L1 is connected to L3, L4, L6, L7, L8
L2 is connected to L3, L4, L5, L7, L8
L3 is connected to L5, L6, L8
L4 is connected to L5, L6, L7
L5 is connected to L7, L8
L6 is connected to L7, L8
answered Jun 9 '17 at 9:03
Evargalo
2,30218
add a comment |Â
up vote
2
down vote
Not sure what part it exactly is you didn't understand:
- how the graph is built:
Each vertex represents a traffic lane. Since you will get an accident if cars from lanes $L_1$ and $L_2$ have green lights at the same time, you draw an edge between $L_1$ and $L_2$ on the graph. Proceed in the same way for each couple of vertices, and all constraints are summed up in the given graph.
- how the solution works:
From the graph, you need do find a coloration: assign a group to each vertex so that vertices in the same group can have green lights at the same time, i.e. there is no edge between two vertices in the same group.
You need at least three groups since $L_2$, $L_4$ and $L_6$ are all connected. The coloration shown solves the problem and has only three groups, so it is minimal.
answered May 31 '17 at 15:21
Evargalo
2,30218
please see the edit.....
– Hello_World
May 31 '17 at 16:42
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
Answering the edit:
In the graph associated to your second example of intersection:
It has 8 vertices (L1 to L8)
Its edges are:
(listing only the links that have not already been mentioned)
L1 is connected to L3, L4, L6, L7, L8
L2 is connected to L3, L4, L5, L7, L8
L3 is connected to L5, L6, L8
L4 is connected to L5, L6, L7
L5 is connected to L7, L8
L6 is connected to L7, L8
answered Jun 9 '17 at 9:03
Evargalo
2,30218
add a comment |Â
up vote
1
down vote
accepted
Answering the edit:
In the graph associated to your second example of intersection:
It has 8 vertices (L1 to L8)
Its edges are:
(listing only the links that have not already been mentioned)
L1 is connected to L3, L4, L6, L7, L8
L2 is connected to L3, L4, L5, L7, L8
L3 is connected to L5, L6, L8
L4 is connected to L5, L6, L7
L5 is connected to L7, L8
L6 is connected to L7, L8
answered Jun 9 '17 at 9:03
Evargalo
2,30218
add a comment |Â
up vote
1
down vote
accepted
up vote
1
down vote
accepted
Answering the edit:
In the graph associated to your second example of intersection:
It has 8 vertices (L1 to L8)
Its edges are:
(listing only the links that have not already been mentioned)
L1 is connected to L3, L4, L6, L7, L8
L2 is connected to L3, L4, L5, L7, L8
L3 is connected to L5, L6, L8
L4 is connected to L5, L6, L7
L5 is connected to L7, L8
L6 is connected to L7, L8
answered Jun 9 '17 at 9:03
Evargalo
2,30218
Answering the edit:
In the graph associated to your second example of intersection:
It has 8 vertices (L1 to L8)
Its edges are:
(listing only the links that have not already been mentioned)
L1 is connected to L3, L4, L6, L7, L8
L2 is connected to L3, L4, L5, L7, L8
L3 is connected to L5, L6, L8
L4 is connected to L5, L6, L7
L5 is connected to L7, L8
L6 is connected to L7, L8
answered Jun 9 '17 at 9:03
Evargalo
2,30218
answered Jun 9 '17 at 9:03
Evargalo
2,30218
answered Jun 9 '17 at 9:03
Evargalo
2,30218
answered Jun 9 '17 at 9:03
Evargalo
2,30218
2,30218
add a comment |Â
add a comment |Â
up vote
2
down vote
Not sure what part it exactly is you didn't understand:
- how the graph is built:
Each vertex represents a traffic lane. Since you will get an accident if cars from lanes $L_1$ and $L_2$ have green lights at the same time, you draw an edge between $L_1$ and $L_2$ on the graph. Proceed in the same way for each couple of vertices, and all constraints are summed up in the given graph.
- how the solution works:
From the graph, you need do find a coloration: assign a group to each vertex so that vertices in the same group can have green lights at the same time, i.e. there is no edge between two vertices in the same group.
You need at least three groups since $L_2$, $L_4$ and $L_6$ are all connected. The coloration shown solves the problem and has only three groups, so it is minimal.
answered May 31 '17 at 15:21
Evargalo
2,30218
please see the edit.....
– Hello_World
May 31 '17 at 16:42
add a comment |Â
up vote
2
down vote
Not sure what part it exactly is you didn't understand:
- how the graph is built:
Each vertex represents a traffic lane. Since you will get an accident if cars from lanes $L_1$ and $L_2$ have green lights at the same time, you draw an edge between $L_1$ and $L_2$ on the graph. Proceed in the same way for each couple of vertices, and all constraints are summed up in the given graph.
- how the solution works:
From the graph, you need do find a coloration: assign a group to each vertex so that vertices in the same group can have green lights at the same time, i.e. there is no edge between two vertices in the same group.
You need at least three groups since $L_2$, $L_4$ and $L_6$ are all connected. The coloration shown solves the problem and has only three groups, so it is minimal.
answered May 31 '17 at 15:21
Evargalo
2,30218
please see the edit.....
– Hello_World
May 31 '17 at 16:42
add a comment |Â
up vote
2
down vote
up vote
2
down vote
Not sure what part it exactly is you didn't understand:
- how the graph is built:
Each vertex represents a traffic lane. Since you will get an accident if cars from lanes $L_1$ and $L_2$ have green lights at the same time, you draw an edge between $L_1$ and $L_2$ on the graph. Proceed in the same way for each couple of vertices, and all constraints are summed up in the given graph.
- how the solution works:
From the graph, you need do find a coloration: assign a group to each vertex so that vertices in the same group can have green lights at the same time, i.e. there is no edge between two vertices in the same group.
You need at least three groups since $L_2$, $L_4$ and $L_6$ are all connected. The coloration shown solves the problem and has only three groups, so it is minimal.
answered May 31 '17 at 15:21
Evargalo
2,30218
Not sure what part it exactly is you didn't understand:
- how the graph is built:
Each vertex represents a traffic lane. Since you will get an accident if cars from lanes $L_1$ and $L_2$ have green lights at the same time, you draw an edge between $L_1$ and $L_2$ on the graph. Proceed in the same way for each couple of vertices, and all constraints are summed up in the given graph.
- how the solution works:
From the graph, you need do find a coloration: assign a group to each vertex so that vertices in the same group can have green lights at the same time, i.e. there is no edge between two vertices in the same group.
You need at least three groups since $L_2$, $L_4$ and $L_6$ are all connected. The coloration shown solves the problem and has only three groups, so it is minimal.
answered May 31 '17 at 15:21
Evargalo
2,30218
answered May 31 '17 at 15:21
Evargalo
2,30218
answered May 31 '17 at 15:21
Evargalo
2,30218
answered May 31 '17 at 15:21
Evargalo
2,30218
2,30218
please see the edit.....
– Hello_World
May 31 '17 at 16:42
add a comment |Â
please see the edit.....
– Hello_World
May 31 '17 at 16:42
please see the edit.....
– Hello_World
May 31 '17 at 16:42
please see the edit.....
– Hello_World
May 31 '17 at 16:42
add a comment |Â
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What part of the explanation is unclear to you? The more specific you are, the more likely it is you'll get the clarification you seek.
– Fabio Somenzi
May 31 '17 at 15:19
I would like to know how the graph is built....
– Hello_World
May 31 '17 at 15:55
That isn't very specific, is it? Have you read the answer by @Evargalo?
– Fabio Somenzi
May 31 '17 at 15:59