some properties of star-perfect graphs

For a finite simple graph $g=(v, e)$, $theta_s(g)$ denotes the minimum number of induced stars contained in $g$ such that the union of their vertex sets is $v(g)$, and $ alpha_s(g)$ denotes the maximum number of vertices in $g$ such that no two are contained in the same induced star of $g$. we call the graph $g$ star-perfect if $alpha_s(h)=theta_s(h)$, for every induced subgraph $h$ of $g$. we prove here that no cycle in a star-perfect graph has crossing chords and star-perfect graphs are planar. also we present a few properties of star perfect graphs.