Geodesic
A linear algorithm for computing the multiclique cover number of a series-parallel graph
Trudy Instituta matematiki, Tome 17 (2009) no. 1, pp. 90-102

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A multiclique is a complete multipartite subgraph of a graph. A multiclique cover of a graph $G$ is a collection of multicliques of $G$ whose edge sets cover the edge set of $G$ (every edge of $G$ belongs to at least one multiclique of the collection). The multiclique cover number, $mc(G)$, of a graph $G$ is the minimum number of multicliques in a multiclique cover of $G$. A linear-time algorithm for computing the multiclique cover number of a (simple) series-parallel graph is given. 
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     title = {A linear algorithm for computing the multiclique cover number of a series-parallel graph},
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V. V. Lepin. A linear algorithm for computing the multiclique cover number of a series-parallel graph. Trudy Instituta matematiki, Tome 17 (2009) no. 1, pp. 90-102. http://geodesic.mathdoc.fr/item/TIMB_2009_17_1_a8/