3 problems

Kotlov–Lovász–Vempala conjecture. For every such graph $G$,

Let $K$ be a $d$-dimensional balanced simplicial complex, and let $<$ be a $(3,\ldots,3)$-admissible order. Let $K^{b,<}$ denote the corresponding balanced shift. Balanced linkless…

Let $G=(A\uplus B,E)$ be a bipartite linklessly embeddable graph, and let $<$ be a $(3,3)$-admissible order. Write $G^b$ for the balanced shift of $G$. Bipartite linkless-embeddabi…