  A graph coloring has bounded clustering if each monochromatic component has
bounded size. This paper studies such a coloring, where the number of colors
depends on an excluded complete bipartite subgraph. This is a much weaker
assumption than previous works, where typically the number of colors depends on
an excluded minor. This paper focuses on graph classes with bounded layered
treewidth, which include planar graphs, graphs of bounded Euler genus, graphs
embeddable on a fixed surface with a bounded number of crossings per edge,
amongst other examples. Our main theorem says that for fixed integers $s,t,k$,
every graph with layered treewidth at most $k$ and with no $K_{s,t}$ subgraph
is $(s+2)$-colorable with bounded clustering. The $s=3$ case implies that every
graph with a drawing on a fixed surface with a bounded number of crossings per
edge is 5-colorable with bounded clustering. Our main theorem is also a
critical component in two companion papers that study clustered coloring of
graphs with no $K_{s,t}$ subgraph and excluding a fixed minor, odd minor or
topological minor.
