DEGREE CONDITIONS AND FRACTIONAL k-FACTORS OF GRAPHS

Title & Authors
DEGREE CONDITIONS AND FRACTIONAL k-FACTORS OF GRAPHS
Zhou, Sizhong;

Abstract
Let k $\small{\geq}$ 1 be an integer, and let G be a 2-connected graph of order n with n $\small{\geq}$ max{7, 4k+1}, and the minimum degree $\small{\delta(G)}$ $\small{\geq}$ k+1. In this paper, it is proved that G has a fractional k-factor excluding any given edge if G satisfies max{$\small{d_G(x)}$, $\small{d_G(y)}$} $\small{\geq}$ $\small{\frac{n}{2}}$ for each pair of nonadjacent vertices x, y of G. Furthermore, it is showed that the result in this paper is best possible in some sense.
Keywords
graph;degree;k-factor;fractional k-factor;
Language
English
Cited by
1.
An existence theorem on fractional deleted graphs, Periodica Mathematica Hungarica, 2015, 71, 1, 125
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