Let　Pn　and　Cn　denote　the　induced　path　and　cycle　on　n　vertices,　respectively.　For　two　graphs　H1　and　H2,　we　use　H1∪H2　to　denote　the　graph　with　vertex　set　V(H1)∪V(H2)　and　edge　set　E(H1)∪E(H2).　Let　Δ(G),　χ(G)　and　ω(G)　denote　the　maximum　degree,　chromatic　number　and　clique　number　of　G,　respectively.　The　Borodin–Kostochka　Conjecture　states　that　for　a　graph　G,　if　Δ(G)≥9,　then　χ(G)≤max{Δ(G)-1,ω(G)}.　In　this　paper,　we　prove　the　conjecture　for　{P2∪P3,C4}-free　graphs.　©　The　Author(s),　under　exclusive　licence　to　Springer　Nature　Japan　KK　2024.