Parthasarathy's theorem
Imagine you have a super tricky maze with lots of paths and you want to know if there is a way to go through all the paths without repeating any. Well, Parthasarathy's theorem says that if the maze is connected and has an even number of paths at each point, then there is a way to go through all the paths without repeating any!
But wait, what's a connected maze? Think of the roads in your neighborhood. If you can get to any house by driving on the roads in your neighborhood, then your neighborhood is connected. Similarly, a maze is called connected if you can get from any point to any other point by walking along the maze's paths.
But what about the even number of paths at each point? Imagine you are at a crossroads in the maze where four paths meet. If there are an odd number of paths passing through this point, then there will be at least one path that you cannot use after you have gone down the other paths. This means you will have to backtrack, and you will end up repeating some of the paths you have already taken. But if there are an even number of paths passing through this point, then you can go down any two paths and then come back to the crossroads and go down the other two paths without repeating any!
So, in summary, Parthasarathy's theorem says that if you have a connected maze with an even number of paths at each point, then there is a way to go through all the paths without repeating any. It's like having a magic trick to solve any maze that follows these conditions!
But wait, what's a connected maze? Think of the roads in your neighborhood. If you can get to any house by driving on the roads in your neighborhood, then your neighborhood is connected. Similarly, a maze is called connected if you can get from any point to any other point by walking along the maze's paths.
But what about the even number of paths at each point? Imagine you are at a crossroads in the maze where four paths meet. If there are an odd number of paths passing through this point, then there will be at least one path that you cannot use after you have gone down the other paths. This means you will have to backtrack, and you will end up repeating some of the paths you have already taken. But if there are an even number of paths passing through this point, then you can go down any two paths and then come back to the crossroads and go down the other two paths without repeating any!
So, in summary, Parthasarathy's theorem says that if you have a connected maze with an even number of paths at each point, then there is a way to go through all the paths without repeating any. It's like having a magic trick to solve any maze that follows these conditions!