Decomposing Graphs of High Minimum Degree into 4-Cycles

  title={Decomposing Graphs of High Minimum Degree into 4-Cycles},
  author={Darryn E. Bryant and Nicholas J. Cavenagh},
  journal={Journal of Graph Theory},
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

From This Paper

Topics from this paper.


Publications citing this paper.

Edge-decompositions of graphs with high minimum degree

Electronic Notes in Discrete Mathematics • 2015
View 2 Excerpts
Highly Influenced


Publications referenced by this paper.
Showing 1-10 of 16 references

The decomposition threshold for bipartite graphs with minimum degree one

Random Struct. Algorithms • 2002
View 5 Excerpts
Highly Influenced

Some theorems on abstract graphs

G. Dirac
Proc. London Math. Soc. (3), 2 • 1952
View 3 Excerpts
Highly Influenced

Packing closed trails into dense graphs

J. Comb. Theory, Ser. B • 2003
View 1 Excerpt

List decomposition of graphs

Discrete Mathematics • 2002
View 1 Excerpt

Tree decomposition of graphs

Random Struct. Algorithms • 1998
View 1 Excerpt

Graph factors and Hamiltonian decompositions

H. Buchanan
PhD Thesis, West Virginia University • 1997
View 1 Excerpt

Decompositions of large graphs and digraphs with high minimum degree

T. Gustavsson
Ph.D Thesis, University of Stockholm • 1991
View 1 Excerpt