Euler Circuit

Euler Circuit is an #202204112129 where there is a cycle that visits every edge exactly once. It has two properties. First, every vertex has a even number of edges. Second, the undirected graph is connected.

A graph could be determined as an Euler Circuit by using #202205021959. This will result in a linear runtime complexity.

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Euler Path

Euler Path, unlike 202205101149, doesn’t need to be a cycle by itself. As long as all edges in the #202204112129 are visited exactly once, the graph is an Euler Path. Like 202205101149, the graph needs to be connected. In the graph, there must be exactly two vertices that has an odd number of edges.
Depth First Search (DFS)

determine 202205101200# and 202205101149#

#graph #math