Generalized graph complexes: the splitting into a complete graph
Résumé
Graph complexes are graded vector spaces of formal linear combinations of isomorphism classes of some kind of graphs, with the differential defined by vertex splitting (or, dually, edge contraction). In this paper a generalization, where vertex splitting (i.e. insertion of the complete graph on two vertices) is replaced by insertion of a complete graph, is introduced. Basic properties are shown.
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