A note on minimum degree conditions for supereulerian graphs

H.J. Broersma, Liming Xiong

Research output: Contribution to journalArticleAcademicpeer-review

15 Citations (Scopus)
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Abstract

A graph is called supereulerian if it has a spanning closed trail. Let G be a 2-edge-connected graph of order n such that each minimal edge cut SE(G) with |S|3 satisfies the property that each component of G−S has order at least (n−2)/5. We prove that either G is supereulerian or G belongs to one of two classes of exceptional graphs. Our results slightly improve earlier results of Catlin and Li. Furthermore, our main result implies the following strengthening of a theorem of Lai within the class of graphs with minimum degree δ4: If G is a 2-edge-connected graph of order n with δ(G)4 such that for every edge xyE(G) , we have max{d(x),d(y)}(n−2)/5−1, then either G is supereulerian or G belongs to one of two classes of exceptional graphs. We show that the condition δ(G)4 cannot be relaxed.
Original languageEnglish
Pages (from-to)35-43
Number of pages9
JournalDiscrete applied mathematics
Volume120
Issue number1-3
DOIs
Publication statusPublished - 2002

Keywords

  • Supereulerian graph
  • Spanning circuit
  • Collapsible graph
  • Degree conditions

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