Postgres 12

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create table lines(
id serial,
colour varchar,
geom geometry(linestring,4326)
);
create table points(
id serial,
colour varchar,
geom geometry(point,4326)
);

insert into lines(colour, geom)
VALUES
('red', st_setsrid(st_makeline(st_makepoint(1,1), st_makepoint(10,1)),4326)),
('green', st_setsrid(st_makeline(st_makepoint(1,1), st_makepoint(10,1)),4326)),
('blue', st_setsrid(st_makeline(st_makepoint(1,1), st_makepoint(10,1)),4326));

insert into points(colour, geom)
VALUES
('red',st_setsrid(st_makepoint(2,1),4326)),
('red',st_setsrid(st_makepoint(4,1),4326)),
('red',st_setsrid(st_makepoint(6,1),4326)),
('red',st_setsrid(st_makepoint(8,1),4326)),
('green',st_setsrid(st_makepoint(2.5,1),4326)),
('green',st_setsrid(st_makepoint(5,1),4326)),
('green',st_setsrid(st_makepoint(7.5,1),4326)),
('blue',st_setsrid(st_makepoint(3,1),4326)),
('blue',st_setsrid(st_makepoint(6,1),4326)),
('blue',st_setsrid(st_makepoint(9,1),4326));

with knife as(
    select st_union(geom) as geom, colour
    from points
    group by colour)
select lines.colour,(st_dump(st_split(lines.geom,knife.geom))).geom as geom
from lines, knife
where lines.colour=knife.colour;

CREATE TABLE

CREATE TABLE

INSERT 0 3

INSERT 0 10

colour	geom
blue	0102000020E6100000020000000000000000002240000000000000F03F0000000000002440000000000000F03F
blue	0102000020E610000002000000000000000000F03F000000000000F03F0000000000000840000000000000F03F
blue	0102000020E6100000020000000000000000000840000000000000F03F0000000000001840000000000000F03F
blue	0102000020E6100000020000000000000000001840000000000000F03F0000000000002240000000000000F03F
green	0102000020E6100000020000000000000000001E40000000000000F03F0000000000002440000000000000F03F
green	0102000020E610000002000000000000000000F03F000000000000F03F0000000000000440000000000000F03F
green	0102000020E6100000020000000000000000000440000000000000F03F0000000000001440000000000000F03F
green	0102000020E6100000020000000000000000001440000000000000F03F0000000000001E40000000000000F03F
red	0102000020E6100000020000000000000000002040000000000000F03F0000000000002440000000000000F03F
red	0102000020E610000002000000000000000000F03F000000000000F03F0000000000000040000000000000F03F
red	0102000020E6100000020000000000000000000040000000000000F03F0000000000001040000000000000F03F
red	0102000020E6100000020000000000000000001040000000000000F03F0000000000001840000000000000F03F
red	0102000020E6100000020000000000000000001840000000000000F03F0000000000002040000000000000F03F

SELECT 13