In ON THE STABLE SET POLYTOPE OF A SERIES-PARALLEL GRAPH from A.R. MAHJOUB (https://link.springer.com/article/10.1007/BF01580723) it is written:
A homeomorph of K4 is a graph obtained from K 4 when its edges are subdivided into paths by inserting new nodes of degree two. Graphs which contain no homeo- morph of K4 as a subgraph are called series-parallel graphs [4].
From this definition i would say yes.
But from the definition in https://en.wikipedia.org/wiki/Series-parallel_graph
i would say no.
What i am missing here?