×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite