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Quasi-Eulerian Hypergraphs
2017
Electronic Journal of Combinatorics
We generalize the notion of an Euler tour in a graph in the following way. An Euler family in a hypergraph is a family of closed walks that jointly traverse each edge of the hypergraph exactly once. An Euler tourthus corresponds to an Euler family with a single component. We provide necessary and sufficient conditions for the existence of an Euler family in an arbitrary hypergraph, and in particular, we show that every 3-uniform hypergraph without cut edges admits an Euler family. Finally, we
doi:10.37236/6361
fatcat:4kqzraw3jvbo5ktmm773xwktz4