A generalization of dirac’s theorem


LetG be an (r+2)-connected graph in which every vertex has degree at leastd and which has at least 2d-r vertices. Then, for any pathQ of lengthr and vertexy not onQ, there is a cycle of length at least 2d-r containing bothQ andy.

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Locke, S.C. A generalization of dirac’s theorem. Combinatorica 5, 149–159 (1985). https://doi.org/10.1007/BF02579378

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AMS subject classification 1980

  • 05 C 38
  • 05 C 40