Decomposing Graphs of High Minimum Degree into 4-Cycles

@article{Bryant2015DecomposingGO,
  title={Decomposing Graphs of High Minimum Degree into 4-Cycles},
  author={Darryn E. Bryant and Nicholas J. Cavenagh},
  journal={Journal of Graph Theory},
  year={2015},
  volume={79},
  pages={167-177}
}
If a graph G decomposes into edge-disjoint 4-cycles, then each vertex of G has even degree and 4 divides the number of edges in G. It is shown that these obvious necessary conditions are also sufficient when G is any simple graph having minimum degree at least ( 32 + on(1))n, where n is the number of vertices in G. This improves the bound given by Gustavsson (1991), who showed (as part of a more general result) sufficiency for simple graphs with minimum degree at least (1−10+on(1))n. On the… CONTINUE READING

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