A special case of completion invariance for the c2 invariant of a graph
Abstract
The c2 invariant is an arithmetic graph invariant defined by Schnetz. It is useful for understanding Feynman periods. Brown and Schnetz conjectured that the c2 invariant has a particular symmetry known as completion invariance. This paper will prove completion invariance of the c2 invariant in the case that p=2 and the completed graph has an odd number of vertices. The methods involve enumerating certain edge bipartitions of graphs; two different constructions are needed.
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