For　graphs　F,G　and　H,　let　F→(G,H)　signify　that　any　red/blue　edge　coloring　of　F　contains　either　a　red　G　or　a　blue　H.　The　Ramsey　number　r(G,H)　is　defined　to　be　the　smallest　integer　r　such　that　Kr→(G,H).　Let　Bn(k)　be　the　book　graph　which　consists　of　n　copies　of　Kk+1　all　sharing　a　common　Kk,　and　let　G:=Kp+1(a1,a2,...,ap+1)　be　the　complete　(p+1)-partite　graph　with　a1=1,　a2|(n−1)　and　ai≤ai+1.　In　this　paper,　avoiding　the　use　of　Szemerédi＇s　regularity　lemma,　we　show　that　for　any　fixed　p≥1,　k≥2　and　sufficiently　large　n,　Kp(n+a∖K1,n+a→(G,Bn(k)).　This　implies　that　the　star-critical　Ramsey　number　r⁎(G,Bn(k))=(p−1)(n+a2k−1)+a2(k−1)+1.　As　a　corollary,　r⁎(G,Bn(k))=(p−1)(n+k−1)+k　for　a1=a2=1　and　ai≤ai+1.　This　solves　a　problem　proposed　by　Hao　and　Lin　(2018)　[11]　in　a　stronger　form.　©　2024