Minimum degree conditions for vertex-disjoint even cycles in large graphs

@article{Chiba2014MinimumDC,
  title={Minimum degree conditions for vertex-disjoint even cycles in large graphs},
  author={Shuya Chiba and Shinya Fujita and Ken-ichi Kawarabayashi and Tadashi Sakuma},
  journal={Adv. Appl. Math.},
  year={2014},
  volume={54},
  pages={105-120}
}
We prove a variant of a theorem of Corradi and Hajnal (1963) [4] which says that if a graph G has at least 3k vertices and its minimum degree is at least 2k, then G contains k vertex-disjoint cycles. Specifically, our main result is the following. For any positive integer k, there is a constant c"k such that if G is a graph with at least c"k vertices and the minimum degree of G is at least 2k, then (i) G contains k vertex-disjoint even cycles, or (ii) (2k-1)K"[email protected]?pK"[email… CONTINUE READING