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Checking for Euler Path

i.A graph has Euler path if exactly two vertices is of odd degree.

if a graph have euler circuit=>all vertices even degree=>euler circuit which already cover euler path. am i correct? i is necessary and sufficient condition?

So for checking Euler path 

we check either

1.Euler Circuit

or 

2.Exactly two odd degree then it will have euler path but not euler circuit.

is it correct?

 

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