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Spanning Eulerian subgraphs in claw-free graphs. (English) Zbl 1124.05054
A finite and loopless graph $$G$$ is called claw-free if it does not contain an induced subgraph isomorphic to $$K_{1,3}$$. $$G$$ is essentially $$k$$-edge-connected if for any edge set $$X$$ with $$| X| <k$$ at most one component of $$G-X$$ has edges. It is shown that every essentially $$4$$-edge-connected claw-free graph $$G$$ has a spanning Eulerian subgraph with maximum degree at most $$4$$.

##### MSC:
 05C45 Eulerian and Hamiltonian graphs