Sizhong Zhou and Hongxia Liu On Fractional (k,m)Deleted Graphs with Constrains Conditions
1081 - 1083
2011
5
7
International Journal of Mathematical and Computational Sciences http://waset.org/publications/3345
http://waset.org/publications/55
World Academy of Science, Engineering and Technology
Let G be a graph of order n, and let k 2 and m 0 be two integers. Let h E(G) 0, 1 be a function. If e∋x h(e) k holds for each x V (G), then we call GFh a fractional kfactor of G with indicator function h where Fh e E(G) h(e) > 0. A graph G is called a fractional (k,m)deleted graph if there exists a fractional kfactor GFh of G with indicator function h such that h(e) 0 for any e E(H), where H is any subgraph of G with m edges. In this paper, it is proved that G is a fractional (k,m)deleted graph if (G) k m m k1 , n 4k2 2k − 6 (4k 2 6k−2)m−2 k−1 and maxdG(x), dG(y) n 2 for any vertices x and y of G with dG(x, y) 2. Furthermore, it is shown that the result in this paper is best possible in some sense.
International Science Index 55, 2011