Recently, Chmutov proved that the partial-dual polynomial considered as a function on chord diagrams satisfies the four-term relations. In this paper, we show that this function on framed chord diagrams also satisfies the four-term relations, i.e., is a framed weight system.

• 05C10 - Planar graphs; geometric and topological aspects of graph theory
• 05C65 - Hypergraphs
• 57M15 - Relations of low-dimensional topology with graph theory
• 57Q15 - Triangulating manifolds