MGF 1107 – EXPLORATIONS IN MATHEMATICS
LECTURE 14
We are now in a position to introduce Euler’s theorem, which is used to
determine if a graph contains Euler paths and Euler circuits.
Euler’s Circuit Theorem
i) If a graph is connected and every vertex is even, then there exists at
least one Euler circuit (which we can start and end at any vertex).
ii) If any graph has an odd vertex then no Euler circuits exist.
Ex.

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