Binding number and minimum degree for the existence of fractional k-factors with prescribed properties

Abstract

Let G be a graph, and let k ≥ 1 be an integer. Let h: E(G) → [0,1] be a function. If Σ _e∋x h(e) = k holds for any x ∈ V(G), then we call G [F _h) a fractional k-factor of G with indicator function h where F _h = {e ∈ E(G): h(e) > 0}. In this paper, we obtain two sufficient conditions for graphs to have fractional k-factors depending on bind(G) and δ(G).