A short proof of the generalized Conway--Gordon--Sachs theorem

2025/02/09 by Nikkuni, Ryo
#57K10 #57M15 #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2502.05930

Abstract

The famous Conway--Gordon--Sachs theorem for the complete graph on six vertices was extended to the general complete graph on n vertices by Kazakov--Korablev as a congruence modulo 2, and its integral lift was given by Morishita--Nikkuni. However, the proof is complicated and long. In this paper, we provide a shorter proof of the generalized Conway--Gordon--Sachs theorem over integers.

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