On representable graphs, semi-transitive orientations, and the representation numbers

Magnus Mar Halldorsson, Sergey Kitaev, Artem Pyatkin

A graph $G=(V,E)$ is representable if there exists a word $W$ over the alphabet $V$ such that letters $x$ and $y$ alternate in $W$ if and only if $(x,y)\in E$ for each $x\ne y$. I…