A special case of completion invariance for the c₂ invariant of a graph

2017/06/27 by Yeats, Karen
#05C31 (primary) 05C30 #81T18 (secondary) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1706.08857

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.

Related

• Completing the c₂ completion conjecture for p=2
• A study on prefixes of c₂ invariants
• A few c₂ invariants of circulant graphs
• Properties of c₂ invariants of Feynman graphs
• The c₂ invariant is invariant