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arXiv · 1905.06895

Switches in Eulerian graphs

Ahad N. Zehmakan·Jerri Nummenpalo·Alexander Pilz·Daniel Wolleb-Graf
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Abstract

We show that the graph transformation problem of turning a simple graph into an Eulerian one by a minimum number of single edge switches is NP-hard. Further, we show that any simple Eulerian graph can be transformed into any other such graph by a sequence of 2-switches (i.e., exchange of two edge pairs), such that every intermediate graph is also Eulerian. However, finding the shortest such sequence also turns out to be an NP-hard problem.

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Ahad N. Zehmakan, Jerri Nummenpalo, Alexander Pilz, Daniel Wolleb-Graf. 2019-05-08. Switches in Eulerian graphs. https://arxiv.org/abs/1905.06895

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