Let G and H be two vertex disjoint graphs. The {\em union} GβͺH is
the graph with V(GβͺH)=V(G)βͺ(H) and E(GβͺH)=E(G)βͺE(H). The
{\em join} G+H is the graph with V(G+H)=V(G)+V(H) and E(G+H)=E(G)βͺE(H)βͺ{xyβ£xβV(G),yβV(H)}. We use Pkβ to denote a {\em
path} on k vertices, use {\em fork} to denote the graph obtained from
K1,3β by subdividing an edge once, and use {\em crown} to denote the graph
K1β+K1,3β. In this paper, we show that (\romannumeral 1)
Ο(G)β€23β(Ο2(G)βΟ(G)) if G is (crown, P5β)-free,
(\romannumeral 2) Ο(G)β€21β(Ο2(G)+Ο(G)) if G is
(crown, fork)-free, and (\romannumeral 3)
Ο(G)β€21βΟ2(G)+23βΟ(G)+1 if G is (crown,
P3ββͺP2β)-free.Comment: arXiv admin note: text overlap with arXiv:2302.0680