Is it possible to arrange the routes and the bus stops so that if one route is closed, it is still possible to get from any one stop to any other [on hold] The Next CEO of Stack Overflow100 roads in a city, 1 is closedA graph on the cities of a countryGraph theory. Cities connected to other cities by roads.Graph Theory-Eulerian Path?Finding number of roadsFinding meeting points in GraphAssigning drivers to buses and routes“A combinations problem.” There are $10$ halting stations on a circular road in a city…Constrained Graph Optimization - Algorithm to connect thousands of nodes while minimizing cost for bus routing?A route that passes through all streets of the city
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Is it possible to arrange the routes and the bus stops so that if one route is closed, it is still possible to get from any one stop to any other [on hold]
The Next CEO of Stack Overflow100 roads in a city, 1 is closedA graph on the cities of a countryGraph theory. Cities connected to other cities by roads.Graph Theory-Eulerian Path?Finding number of roadsFinding meeting points in GraphAssigning drivers to buses and routes“A combinations problem.” There are $10$ halting stations on a circular road in a city…Constrained Graph Optimization - Algorithm to connect thousands of nodes while minimizing cost for bus routing?A route that passes through all streets of the city
$begingroup$
A certain City has 10bus routes. Is it possible to arrange the routes and the bus stops so that if one route is closed, it is still possible to get from any one stop to any other, but if any two routes are closed, there are at least two stops such that it is impossible to get from one to the other?
graph-theory combinations projective-geometry geometric-topology
asked 2 days ago
Kazi Abu RousanKazi Abu Rousan
12
$endgroup$
put on hold as off-topic by Crostul, zz20s, Leucippus, dantopa, Abcd yesterday
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Crostul, zz20s, Leucippus, dantopa, Abcd
add a comment |
$begingroup$
A certain City has 10bus routes. Is it possible to arrange the routes and the bus stops so that if one route is closed, it is still possible to get from any one stop to any other, but if any two routes are closed, there are at least two stops such that it is impossible to get from one to the other?
graph-theory combinations projective-geometry geometric-topology
asked 2 days ago
Kazi Abu RousanKazi Abu Rousan
12
$endgroup$
put on hold as off-topic by Crostul, zz20s, Leucippus, dantopa, Abcd yesterday
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Crostul, zz20s, Leucippus, dantopa, Abcd
$begingroup$
Tags are inappropriate. I suggest to modify the tags as topology or graphs
$endgroup$
– Crostul
2 days ago
$begingroup$
Thank you sir but it is a exercise of projective geometry so I use those tages....I changed those
$endgroup$
– Kazi Abu Rousan
2 days ago
$begingroup$
Please explain your problem. In particular, are the bus stops at the interceptions of the routes?
$endgroup$
– Ertxiem
2 days ago
$begingroup$
Sir there are not more information other than that statement. it is from here books.google.co.in/… problem 101( page 4)
$endgroup$
– Kazi Abu Rousan
2 days ago
add a comment |
$begingroup$
A certain City has 10bus routes. Is it possible to arrange the routes and the bus stops so that if one route is closed, it is still possible to get from any one stop to any other, but if any two routes are closed, there are at least two stops such that it is impossible to get from one to the other?
graph-theory combinations projective-geometry geometric-topology
asked 2 days ago
Kazi Abu RousanKazi Abu Rousan
12
$endgroup$
A certain City has 10bus routes. Is it possible to arrange the routes and the bus stops so that if one route is closed, it is still possible to get from any one stop to any other, but if any two routes are closed, there are at least two stops such that it is impossible to get from one to the other?
graph-theory combinations projective-geometry geometric-topology
graph-theory combinations projective-geometry geometric-topology
asked 2 days ago
Kazi Abu RousanKazi Abu Rousan
12
asked 2 days ago
Kazi Abu RousanKazi Abu Rousan
12
edited 2 days ago
Kazi Abu Rousan
asked 2 days ago
Kazi Abu RousanKazi Abu Rousan
12
asked 2 days ago
Kazi Abu RousanKazi Abu Rousan
12
asked 2 days ago
Kazi Abu RousanKazi Abu Rousan
12
12
put on hold as off-topic by Crostul, zz20s, Leucippus, dantopa, Abcd yesterday
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Crostul, zz20s, Leucippus, dantopa, Abcd
put on hold as off-topic by Crostul, zz20s, Leucippus, dantopa, Abcd yesterday
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Crostul, zz20s, Leucippus, dantopa, Abcd
$begingroup$
Tags are inappropriate. I suggest to modify the tags as topology or graphs
$endgroup$
– Crostul
2 days ago
$begingroup$
Thank you sir but it is a exercise of projective geometry so I use those tages....I changed those
$endgroup$
– Kazi Abu Rousan
2 days ago
$begingroup$
Please explain your problem. In particular, are the bus stops at the interceptions of the routes?
$endgroup$
– Ertxiem
2 days ago
$begingroup$
Sir there are not more information other than that statement. it is from here books.google.co.in/… problem 101( page 4)
$endgroup$
– Kazi Abu Rousan
2 days ago
add a comment |
$begingroup$
Tags are inappropriate. I suggest to modify the tags as topology or graphs
$endgroup$
– Crostul
2 days ago
$begingroup$
Thank you sir but it is a exercise of projective geometry so I use those tages....I changed those
$endgroup$
– Kazi Abu Rousan
2 days ago
$begingroup$
Please explain your problem. In particular, are the bus stops at the interceptions of the routes?
$endgroup$
– Ertxiem
2 days ago
$begingroup$
Sir there are not more information other than that statement. it is from here books.google.co.in/… problem 101( page 4)
$endgroup$
– Kazi Abu Rousan
2 days ago
$begingroup$
Tags are inappropriate. I suggest to modify the tags as topology or graphs
$endgroup$
– Crostul
2 days ago
$begingroup$
Tags are inappropriate. I suggest to modify the tags as topology or graphs
$endgroup$
– Crostul
2 days ago
$begingroup$
Thank you sir but it is a exercise of projective geometry so I use those tages....I changed those
$endgroup$
– Kazi Abu Rousan
2 days ago
$begingroup$
Thank you sir but it is a exercise of projective geometry so I use those tages....I changed those
$endgroup$
– Kazi Abu Rousan
2 days ago
$begingroup$
Please explain your problem. In particular, are the bus stops at the interceptions of the routes?
$endgroup$
– Ertxiem
2 days ago
$begingroup$
Please explain your problem. In particular, are the bus stops at the interceptions of the routes?
$endgroup$
– Ertxiem
2 days ago
$begingroup$
Sir there are not more information other than that statement. it is from here books.google.co.in/… problem 101( page 4)
$endgroup$
– Kazi Abu Rousan
2 days ago
$begingroup$
Sir there are not more information other than that statement. it is from here books.google.co.in/… problem 101( page 4)
$endgroup$
– Kazi Abu Rousan
2 days ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
If we are free to decide how many stops we have and how they are arranged then the following is a solution to the problem although totally impractical as a bus network.
Arrange ten stops in a circle, and have each bus route run between two neighbouring stops (so there are just two stops on each route, and each stop is served by just two different routes). If one route is removed there is still a route between the two stops that it served - by going "the long way round" using all the other routes. But if two routes are removed then the graph of routes and stops becomes disconnected.
answered 2 days ago
gandalf61gandalf61
9,174825
$endgroup$
$begingroup$
What is the removed routes are adjacent? Perhaps with 20 points and 2 shared bus stops is enough...
$endgroup$
– Ertxiem
yesterday
$begingroup$
If the removed routes are adjacent then the stop that is shared by those two routes is now unreachable from any other stop, as no other routes serve that stop.
$endgroup$
– gandalf61
yesterday
$begingroup$
You're right, I was overcomplicating the problem (I was thinking that 2 stops needed to be unreachable when is enough that only one is unreachable in this case).
$endgroup$
– Ertxiem
19 hours ago
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
If we are free to decide how many stops we have and how they are arranged then the following is a solution to the problem although totally impractical as a bus network.
Arrange ten stops in a circle, and have each bus route run between two neighbouring stops (so there are just two stops on each route, and each stop is served by just two different routes). If one route is removed there is still a route between the two stops that it served - by going "the long way round" using all the other routes. But if two routes are removed then the graph of routes and stops becomes disconnected.
answered 2 days ago
gandalf61gandalf61
9,174825
$endgroup$
$begingroup$
What is the removed routes are adjacent? Perhaps with 20 points and 2 shared bus stops is enough...
$endgroup$
– Ertxiem
yesterday
$begingroup$
If the removed routes are adjacent then the stop that is shared by those two routes is now unreachable from any other stop, as no other routes serve that stop.
$endgroup$
– gandalf61
yesterday
$begingroup$
You're right, I was overcomplicating the problem (I was thinking that 2 stops needed to be unreachable when is enough that only one is unreachable in this case).
$endgroup$
– Ertxiem
19 hours ago
add a comment |
$begingroup$
If we are free to decide how many stops we have and how they are arranged then the following is a solution to the problem although totally impractical as a bus network.
Arrange ten stops in a circle, and have each bus route run between two neighbouring stops (so there are just two stops on each route, and each stop is served by just two different routes). If one route is removed there is still a route between the two stops that it served - by going "the long way round" using all the other routes. But if two routes are removed then the graph of routes and stops becomes disconnected.
answered 2 days ago
gandalf61gandalf61
9,174825
$endgroup$
$begingroup$
What is the removed routes are adjacent? Perhaps with 20 points and 2 shared bus stops is enough...
$endgroup$
– Ertxiem
yesterday
$begingroup$
If the removed routes are adjacent then the stop that is shared by those two routes is now unreachable from any other stop, as no other routes serve that stop.
$endgroup$
– gandalf61
yesterday
$begingroup$
You're right, I was overcomplicating the problem (I was thinking that 2 stops needed to be unreachable when is enough that only one is unreachable in this case).
$endgroup$
– Ertxiem
19 hours ago
add a comment |
$begingroup$
If we are free to decide how many stops we have and how they are arranged then the following is a solution to the problem although totally impractical as a bus network.
Arrange ten stops in a circle, and have each bus route run between two neighbouring stops (so there are just two stops on each route, and each stop is served by just two different routes). If one route is removed there is still a route between the two stops that it served - by going "the long way round" using all the other routes. But if two routes are removed then the graph of routes and stops becomes disconnected.
answered 2 days ago
gandalf61gandalf61
9,174825
$endgroup$
If we are free to decide how many stops we have and how they are arranged then the following is a solution to the problem although totally impractical as a bus network.
Arrange ten stops in a circle, and have each bus route run between two neighbouring stops (so there are just two stops on each route, and each stop is served by just two different routes). If one route is removed there is still a route between the two stops that it served - by going "the long way round" using all the other routes. But if two routes are removed then the graph of routes and stops becomes disconnected.
answered 2 days ago
gandalf61gandalf61
9,174825
answered 2 days ago
gandalf61gandalf61
9,174825
answered 2 days ago
gandalf61gandalf61
9,174825
answered 2 days ago
gandalf61gandalf61
9,174825
9,174825
$begingroup$
What is the removed routes are adjacent? Perhaps with 20 points and 2 shared bus stops is enough...
$endgroup$
– Ertxiem
yesterday
$begingroup$
If the removed routes are adjacent then the stop that is shared by those two routes is now unreachable from any other stop, as no other routes serve that stop.
$endgroup$
– gandalf61
yesterday
$begingroup$
You're right, I was overcomplicating the problem (I was thinking that 2 stops needed to be unreachable when is enough that only one is unreachable in this case).
$endgroup$
– Ertxiem
19 hours ago
add a comment |
$begingroup$
What is the removed routes are adjacent? Perhaps with 20 points and 2 shared bus stops is enough...
$endgroup$
– Ertxiem
yesterday
$begingroup$
If the removed routes are adjacent then the stop that is shared by those two routes is now unreachable from any other stop, as no other routes serve that stop.
$endgroup$
– gandalf61
yesterday
$begingroup$
You're right, I was overcomplicating the problem (I was thinking that 2 stops needed to be unreachable when is enough that only one is unreachable in this case).
$endgroup$
– Ertxiem
19 hours ago
$begingroup$
What is the removed routes are adjacent? Perhaps with 20 points and 2 shared bus stops is enough...
$endgroup$
– Ertxiem
yesterday
$begingroup$
What is the removed routes are adjacent? Perhaps with 20 points and 2 shared bus stops is enough...
$endgroup$
– Ertxiem
yesterday
$begingroup$
If the removed routes are adjacent then the stop that is shared by those two routes is now unreachable from any other stop, as no other routes serve that stop.
$endgroup$
– gandalf61
yesterday
$begingroup$
If the removed routes are adjacent then the stop that is shared by those two routes is now unreachable from any other stop, as no other routes serve that stop.
$endgroup$
– gandalf61
yesterday
$begingroup$
You're right, I was overcomplicating the problem (I was thinking that 2 stops needed to be unreachable when is enough that only one is unreachable in this case).
$endgroup$
– Ertxiem
19 hours ago
$begingroup$
You're right, I was overcomplicating the problem (I was thinking that 2 stops needed to be unreachable when is enough that only one is unreachable in this case).
$endgroup$
– Ertxiem
19 hours ago
add a comment |
$begingroup$
Tags are inappropriate. I suggest to modify the tags as topology or graphs
$endgroup$
– Crostul
2 days ago
$begingroup$
Thank you sir but it is a exercise of projective geometry so I use those tages....I changed those
$endgroup$
– Kazi Abu Rousan
2 days ago
$begingroup$
Please explain your problem. In particular, are the bus stops at the interceptions of the routes?
$endgroup$
– Ertxiem
2 days ago
$begingroup$
Sir there are not more information other than that statement. it is from here books.google.co.in/… problem 101( page 4)
$endgroup$
– Kazi Abu Rousan
2 days ago