How can I find Eulerian paths in a graph?
An example of an AI chatbot conversation about finding Eulerian paths in graphs.
What is an Eulerian path?
An Eulerian path is a trail in a graph that visits every edge exactly once. It can start and end at different vertices.
How do I determine if a graph has an Eulerian path?
A graph has an Eulerian path if it has exactly zero or two vertices of odd degree. All other vertices must have even degree.
Can you give me an example of finding an Eulerian path?
Sure! Consider a graph with vertices A, B, and C, and edges AB, AC, and BC. This graph has an Eulerian path: A -> B -> C -> A.
What if the graph has more than two odd degree vertices?
If a graph has more than two odd degree vertices, it cannot have an Eulerian path. You would need to add edges to make the degrees even.
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