Elsevier

Discrete Mathematics

Volume 160, Issues 1–3, 15 November 1996, Pages 81-91
Discrete Mathematics

Regular paper
Graphs without spanning closed trails

https://doi.org/10.1016/S0012-365X(95)00149-QGet rights and content
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Abstract

Jaeger (1979) proved that if a graph has two edge-disjoint spanning trees, then it is supereulerian, i.e., that it has a spanning closed trail. Catlin (1988) showed that if G is one edge short of having two edge-disjoint spanning trees, then G has a cut edge or G is supereulerian. Catlin conjectured that if a connected graph G is at most two edges short of having two edge-disjoint spanning trees, then either G is supereulerian or G can be contracted to a K2 or a K2,t for some odd integer t ⩾ 1. We prove Catlin's conjecture in a more general context. Applications to spanning trails are discussed.

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Sadly, the author passed away on April 20, 1995.

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Partially supported by ONR grant N00014-91-J-1699.