Super-Eulerian graphs and the Petersen graph. II (Q2715961)
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scientific article; zbMATH DE number 1600932
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Super-Eulerian graphs and the Petersen graph. II |
scientific article; zbMATH DE number 1600932 |
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30 May 2001
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Eulerian graph
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super-Eulerian graph
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Petersen graph
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Super-Eulerian graphs and the Petersen graph. II (English)
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A graph is called super-Eulerian, if it has an Eulerian (i.e. connected and such that all of its vertices have even degrees) graph as a spanning subgraph. The main result of the paper states that if in a 3-edge-connected graph \(G\) with \(n>306\) vertices for each edge the sum of degrees of its end vertices is at least \(n/6+2\), then either \(G\) is super-Eulerian, or \(G\) can be contracted to the Petersen graph.
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