On (s,t)-Supereulerian Triangle Free Graphs

For two integers s ges 0 and t ges 0, G is (s,t)-supereulerian, if for every two disjoint edge-sets X sub E(G) and Y sub E(G), with |X| les s and |Y| les t, G has a spanning eulerian subgraph H with X sub E(H) and Y cap E(H) = 0. Clearly, G is supereulerian if and only if G is (0,0)-supereulerian. Here it is proved that if G is a (2 + t)-edge-connected triangle-free simple graph on n vertices with delta (G) ges n/10 + t, then when n ges 41 and t ges 1, G is (2, t)-supereulerian or can be contracted to some well classified special graphs. This result extends the result in [Journal of Graph Theory 12 (1988) 11-15].