Eulerian
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- adjective
- /ˈɔɪlərɪən/
- Specialized
- An Eulerian circuit exists in this graph because you can return to the starting point after visiting every edge exactly once.
Examples
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Write a function that takes in a graph represented as a list of tuples and returns a list of nodes that you would follow on an Eulerian Tour.
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It'll be able to show you an Eulerian path (which is different from an Eulerian tour, which has to start and end on the same node).
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A possible Eulerian tour would be 1, 2, 3, 1.
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You will get a planar Eulerian tour, standard trick.
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We just need to figure out how to travel what mathematicians call an Eulerian path, which traces every edge exactly once.
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It'll be able to show you an Eulerian path (which is different from an Eulerian tour, which has to start and end on the same node).
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Moore and Mertens begin with some simple and intuitive problems on graphs, determining whether there exists an Eulerian path, traversing every edge once, and whether there exists a Hamiltonian path, visiting every node once.
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To solve the problem, we need to find an Eulerian trail that visits every edge without repeating any.
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In graph theory, a graph that allows for an Eulerian path must have vertices of even degree, ensuring every edge is covered once.
Synonyms
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A single line you can draw without lifting your pen
Surface Forms
Morphology
Eulerian = Euler (transparent) = Euler + ian
Formed by the regular adjectival suffix '-ian' on the proper name 'Euler', so the relation 'relating to Euler' is morphologically straightforward even though the precise technical content is specialized.
Etymology
Eulerian comes from the name Euler, a Swiss mathematician who solved the famous problem of walking over seven bridges without crossing any bridge twice; imagine a walk that uses each bridge once. So an Eulerian graph is one where you can make a walk or circuit that uses every edge exactly once.