How to Eulerize a graph?
Understand the Problem
The question is asking about the process of Eulerizing a graph, which involves converting it into an Eulerian graph. An Eulerian graph has a trail that visits every edge exactly once. The question likely seeks to understand the steps or methods involved in this transformation, usually related to adding edges to create vertices of even degree.
Answer
Duplicate edges to connect odd degree vertices.
To eulerize a graph, you need to duplicate edges to connect pairs of vertices with odd degrees, turning them into even degrees.
Answer for screen readers
To eulerize a graph, you need to duplicate edges to connect pairs of vertices with odd degrees, turning them into even degrees.
More Information
Eulerizing effectively prepares a graph for finding an Eulerian circuit by ensuring all vertices have even degrees.
Tips
A common mistake in Eulerizing graphs is failing to ensure all odd degree vertices are correctly paired. Verify all vertex degrees are even after modifications.
Sources
- Math LibreTexts: Eulerization and the Chinese Postman Problem - math.libretexts.org
- Euler Circuits | Mathematics for the Liberal Arts - courses.lumenlearning.com
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