Partition of a travel into circuits (Q2774164)
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scientific article; zbMATH DE number 1713429
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Partition of a travel into circuits |
scientific article; zbMATH DE number 1713429 |
Statements
20 May 2002
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circuit partition
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travel
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Eulerian graph
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0.84945357
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0.8115163
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0.8023432
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0.80003387
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Partition of a travel into circuits (English)
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Let \(G\) be a multigraph without loops. A trail between two vertices \(u\) and \(v\) in \(G\) is a sequence \(u=v_1,e_1,v_2,e_2,v_3,\dots,v\) such that \(e_i=v_iv_{i+1}\), \(i=1,2,\dots,l\). When \(u=v\), the trail is called a travel. A travel with pairwise distinct vertices is called a circuit. In this paper a sufficient condition to partition a travel into circuits of length at least 3 is provided. Moreover, a necessary and sufficient condition to partition a planar travel into such circuits, which can be verified in polynomial time, is provided.
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