With　the　rapid　development　of　wireless　networks,　the　burden　on　data　transmission　is　becoming　much　higher,　so　are　the　requirements　for　bandwidth　and　load　balancing.　To　cope　with　these　changing　requirements,　we　investigate　a　novel　problem　of　finding　maximum　disjoint　paths　with　different　colors　(MDPDC).　In　MDPDC,　transmission　frequencies　in　a　network　are　modeled　as　different　colors　on　network　nodes.　The　aim　is　to　find　a　maximum　number　of　color-constrained　node-disjoint　paths　where　nodes　must　share　the　same　color　within　any　disjoint　path,　and　differ　in　color　among　different　disjoint　paths.　For　this　proposed　problem,　we　first　prove　MDPDC　is　NP-complete　in　both　directed　and　undirected　graphs.　Then　we　provide　two　practical　linear　programming　based　solutions　with　theoretical　justifications　of　their　correctness　and　time　complexity.　Extensive　computer　experiments　are　also　carried　out　with　several　compared　baseline　methods　to　demonstrate　the　effectiveness　of　proposed　algorithms　both　in　running　time　and　solution　quality.　©　2021　Elsevier　B.V.