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We prove a new signed elementary symmetric function expansion of thechromatic symmetric function of any unit interval graph. We then usesign-reversing involutions to prove new combinatorial formulas for manyfamilies of graphs, including the K-chains studied by Gebhard and Sagan, formedby joining cliques at single vertices, and for graphs obtained from them byremoving any number of edges from any of the cut vertices. We also introduce aversion for the quasisymmetric refinement of Shareshian and Wachs.

A signed $e$-expansion of the chromatic symmetric function and some new $e$-positive graphs