On the maximal number of independent circuits in a graph

@article{Dirac1963OnTM,
  title={On the maximal number of independent circuits in a graph},
  author={G. A. Dirac and Paul L. Erdos},
  journal={Acta Mathematica Academiae Scientiarum Hungarica},
  year={1963},
  volume={14},
  pages={79-94}
}
  • G. Dirac, P. Erdos
  • Published 1 March 1963
  • Mathematics
  • Acta Mathematica Academiae Scientiarum Hungarica
In a recent paper [l] K . CORRÁDI and A. HAJNAL proved that if a finite graph without multiple edges contains at least 3k vertices and the valency of every vertex is at least 2k, where k is a positive integer, then the graph contains k independent circuits, i . e . the graph contains as a subgraph a set of k circuits no two of which have a vertex in common . The present paper contains extensions of this theorem. In a recent paper [2] P . ERDŐS and L. PÓSA proved, among other things, that if a… 
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References

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On the maximal number of disjoint circuits of a graph
Throughout this paper Gg" will denote a graph with n vertices and k edges where circuits consisting of two edges and loops (i . e. circuits of one edge) are not permitted and G'" will denote a graph
On the maximal number of independent circuits in a graph
In a recent paper [l] K . CORRADI and A. HAJNAL proved that if a finite graph without multiple edges contains at least 3k vertices and the valency of every vertex is at least 2k, where k is a