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

  • Authors:

  • Bin Wang;Xiao-Min Li;Lan Lei

  • Affiliations:

  • The faculty of science, Chongqing Technology, and Business University, Chongqing, 400067, P.R. China;The faculty of science, Chongqing Technology, and Business University, Chongqing, 400067, P.R. China;The faculty of science, Chongqing Technology, and Business University, Chongqing, 400067, P.R. China

  • Venue:
  • ICCS '07 Proceedings of the 7th international conference on Computational Science, Part III: ICCS 2007
  • Year:
  • 2007

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Abstract

For two integers s 驴 0, t 驴 0, G is (s, t)-superlerian, if 驴 X, Y 驴 E(G) with X 驴 Y = 驴, where |X| ≤ s, |Y| ≤ t, G has a spanning eulerian subgraph H such that X 驴 E(H) and Y 驴 E(H) = 驴. 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 驴 21 and $\delta(G)\geq \frac{n}{5}+t$, then G is (3, t)-supererlerian or can be contracted to some well classified special graphs.