Cycles containing all the odd-degree vertices

Kathie Cameron, Carsten Thomassen

Research output: Contribution to journalJournal articleResearchpeer-review


The number of cycles in a graph containing any fixed edge and also containing all vertices of odd degree is odd if and only if all vertices have even degree. If all vertices have even degree this is a theorem of Shunichi Toida. If all vertices have odd degree it is Andrew Thomason's extension of Smith's theorem.

Original languageEnglish
JournalJournal of Combinatorial Theory. Series B
Pages (from-to)219-225
Publication statusPublished - 1 Jan 2020


  • Eulerian graph
  • Hamiltonian cycle
  • Lifting a vertex
  • Parity theorem

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