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A graph is supereulerian if it has a spanning eulerian subgraph. There is a reduction method to determine whether a graph is su-pereulerian, and it can also be applied to study other concepts, e.g., hamiltonian line graphs, a certain type of double cycle cover, and the total interval number of a graph. We outline the research on supereu-lerian graphs, the… (More)

Jaeger [J. Graph Theory 3 (1979) 91-93] 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 [J. Graph Theory 12 (1988) 29-45] 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… (More)

Any 3-edge-connected graph with at most 10 edge cuts of size 3 either has a spanning closed trail or it is contractible to the Petersen graph. 1996 Academic Press, Inc.

Given a graph G, for an integer c