Eulerian path

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Eulerian path

[ȯi′ler·ē·ən ′path]
(mathematics)
A path that traverses each of the lines in a graph exactly once.
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A well-known theorem states that a graph has an Euler path if and only if the number of nodes with odd degree is two or fewer.
Anil comments "Eric Iverson arbitrarily assumed that R is not an Euler Path letter.
A well-known theorem in graph theory states that a network contains an Euler Path (a path that traverses the network, once only along each link) if and only if it has at most two nodes with an odd number of links.
If one posits a sans-serif alphabet, the Euler Path letters (ones that can be traced out without lifting pencil from paper) are BCDGIJLMNOPQSUVWZ.
One can also construct words with no Euler Path letters, the longest being THEREAFTER.