Path Cover in $K_{1,4}$Free Graphs 
Received:July 17, 2018 Revised:October 26, 2018 
Key Word:
path cover path cover number $K_{1,4}$free graph noninsertable vertex

Fund ProjectL:Supported by the Joint Fund of Liaoning Provincial Natural Science Foundation (Grant No.SY2016012). 

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Abstract: 
For a graph $G,$ a path cover is a set of vertex disjoint paths covering all the vertices of $G$, and a path cover number of $G,$ denoted by $p(G),$ is the minimum number of paths in a path cover among all the path covers of $G.$ In this paper, we prove that if $G$ is a $K_{1,4}$free graph of order $n$ and $\sigma_{k+1}(G)\geq {nk}$, then $p(G)\leq k$, where $\sigma_{k+1}(G)=\min\{\sum_{v\in S}{\rm d}(v):S$ is an independent set of $G$ with $S=k+1\}$. 
Citation: 
DOI:10.3770/j.issn:20952651.2019.03.011 
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