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[Maximum mark: 6]

Thomas, a train enthusiast, wants to take every major train in America. He makes a graph with vertices representing cities and edges representing train rides. Trains only go one direction, so he uses a directed graph. Each edge has weight 1.

State whether there exists an Eulerian circuit for this graph. State your reasoning.
[2]

Thomas, the train enthusiast, lives in New York. Hence, he will start and end his train trip in New York.

Find the shortest path from New York to Boston.
[1]
America Rail would like to make the graph contain an Eulerian circuit by flipping the directions of as few edges as possible.
1. Find the edge that they should flip
  [2]
2. Find an Eulerian circuit starting with the train NY→LA.
  [1]

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[Maximum mark: 6]

State whether there exists an Eulerian circuit for this graph. State your reasoning.
[2]

Thomas, the train enthusiast, lives in New York. Hence, he will start and end his train trip in New York.

Find the shortest path from New York to Boston.
[1]
America Rail would like to make the graph contain an Eulerian circuit by flipping the directions of as few edges as possible.
1. Find the edge that they should flip
  [2]
2. Find an Eulerian circuit starting with the train NY→LA.
  [1]

Ask Plex AI about this problem

Get hints, ask questions, and work through this problem step by step

I'm Plex, here to help with problems on this worksheet!