Eulerian subgraphs containing given edges

For an integer l¿0, de ne SE(l) to be the family of graphs such that G ∈SE(l) if and only if for any edge subset X ⊆E(G) with |X |6l, G has a spanning eulerian subgraph H with X ⊆E(H). The graphs in SE(0) are known as supereulerian graphs. Let f(l) be the minimum value of k such that every k-edge-connected graph is in SE(l). Jaeger and Catlin independently proved f(0) = 4. We shall determine f(l) for all values of l¿0. Another problem concerning the existence of eulerian subgraphs containing given edges is also discussed, and former results in [J. Graph Theory 1 (1977) 79–84] and [J. Graph Theory 3 (1979) 91–93] are extended. c © 2001 Elsevier Science B.V. All rights reserved.