A Degree-Condition for (s, t)-Supereulerian Graphs

摘要

For two integers s ≥ 0, t ≥ 0, G is (s, t)-superlerian, if anyX, Y is contained in E(G) with X ∩ Y = φ, where |X| ≤ s, |Y| ≤t,G has a spanning eulerian subgraph H such that X is contained in E(H) and Y ∩ E(H) = φ. It is obvious that G is supereulerian if and only if G is (0, 0)-supereulerian. In this note, we have proved that when G is a (t + 2)-edge-connected simple graph on n vertices, if n ≥ 21 and δ(G) ≥n/5 +t, then G is (3, t)-supererlerian or can be contracted to some well classified special graphs.