Switches in Eulerian graphs
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2019
- DOI:
- 10.48550/arXiv.1905.06895
- arXiv:
- arXiv:1905.06895
- Bibcode:
- 2019arXiv190506895Z
- Keywords:
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- Computer Science - Data Structures and Algorithms;
- Computer Science - Discrete Mathematics;
- Mathematics - Combinatorics