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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

Provided by:
Durham Research Online

Downloaded from
http://dro.dur.ac.uk/7426/1/7426.pdf

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