For　a　positive　integer　n,　we　use　Kn　and　Pn　to　denote　a　complete　graph　and　an　induced　path　on　n　vertices,　respectively.　A　subdivision　of　G　is　a　graph　obtained　from　G　by　replacing　the　edges　of　G　with　independent　paths　of　length　at　least　one　between　their　end　vertices.　A　graph　is　said　to　be　ISK4-free　if　it　does　not　contain　any　subdivision　of　K4　as　an　induced　subgraph.　Lévêque,　Maffray　and　Trotignon　conjectured　that　every　ISK4-free　graph　is　4-colorable.　In　this　paper,　we　show　that　this　conjecture　is　true　for　the　class　of　P6-free　graphs.　©　2023　Elsevier　B.V.