The existence of k-factors in squares of graphs

Let G be a simple connected graph and k a positive integer such that (i) k|V(G)| is even, (ii) @d(G)>=k. Then G^2 contains a k-factor.

[1]  Uppaluri S. R. Murty,et al.  Graph Theory with Applications , 1978 .

[2]  A. M. Hobbs.  Some Hamiltonian results in powers of graphs , 1973 .

[3]  J. A. Bondy,et al.  Graph Theory with Applications , 1978 .

[4]  H. Whitney.  Non-Separable and Planar Graphs. , 1931, Proceedings of the National Academy of Sciences of the United States of America.

[5]  Y. Alavi,et al.  The existence of 2-factors in squares of graphs , 1975 .

[6]  Vasek Chvátal,et al.  Tough graphs and hamiltonian circuits , 1973, Discret. Math..

[7]  W. T. Tutte.  The Factors of Graphs , 1952, Canadian Journal of Mathematics.

[8]  J. A. Bondy,et al.  Graph Theory with Applications , 1978 .

[9]  Hikoe Enomoto,et al.  Toughness and the existence of k-factors , 1985, J. Graph Theory.

[10]  P. Katerinis.  Toughness of graphs and the existence of factors , 1990, Discret. Math..