Imbalance conjecture
The imbalance conjecture is an open problem in graph theory concerning whether edge imbalance sequences are graphic, first formally stated by Kozerenko and Skochko in 2014. == Definitions == For a simple undirected graph G {\displaystyle G} , the imbalance of an edge e = u v {\displaystyle e=uv} is defined as: imb ( e ) = | deg ( u ) − deg ( v ) | {\displaystyle {\text{imb}}(e)=|\deg(u)-\deg(v)|} where deg ( u ) {\displaystyle \deg(u)} and deg ( v ) {\displaystyle \deg(v)} denote the degrees of vertices u {\displaystyle u} and v {\displaystyle v} respectively.