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Cycles through specified vertices in triangle-free graphs.

By Daniel Paulusma and K. Yoshimito


Let G be a triangle-free graph with δ(G) ≥ 2 and σ4(G) ≥ |V(G)|+2. Let S ⊂ V(G) consist of less than σ4/4+ 1 vertices. We prove the following. If all vertices of S have degree at least three, then there exists a cycle C containing S. Both the upper bound on |S| and the lower bound on σ4 are best possible

Topics: Cycle, Path, Triangle-free graph.
Publisher: Zielona Gora, Technical University Press
Year: 2007
OAI identifier: oai:dro.dur.ac.uk.OAI2:7426

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  9. (1984). Dominating cycles in bipartite graphs, in:
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  12. (1989). Long cycles through speci¯ed vertices in a graph,
  13. (1980). Longest Paths and Cycles in Graphs of High Degree,
  14. (1960). Note on hamiltonian circuits,
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