TY - JFULL
AU - Sizhong Zhou and Hongxia Liu
PY - 2011/8/
TI - On Fractional (k,m)-Deleted Graphs with Constrains Conditions
T2 - International Journal of Mathematical and Computational Sciences
SP - 1080
EP - 1083
VL - 5
SN - 1307-6892
UR - https://publications.waset.org/pdf/3345
PU - World Academy of Science, Engineering and Technology
NX - Open Science Index 55, 2011
N2 - 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 G[Fh] a fractional k-factor 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 k-factor G[Fh] 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 k+1 , n 4k2 + 2k − 6 + (4k 2 +6k−2)m−2 k−1 and max{dG(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.
ER -