Series–parallel chromatic hypergraphs

In this paper two-terminal series–parallel chromatic hypergraphs are introduced and for this class of hypergraphs it is shown that the chromatic polynomial can be computed with polynomial complexity. It is also proved that hh-uniform multibridge hypergraphs θ(h;a1,a2,…,ak)θ(h;a1,a2,…,ak) are chromatically unique for h≥3h≥3 if and only if h=3h=3 and a1=a2=⋯=ak=1a1=a2=⋯=ak=1, i.e., when they are sunflower hypergraphs having a core of cardinality 2 and all petals being singletons.