On Representable Graphs

  title={On Representable Graphs},
  author={Sergey Kitaev and Artem V. Pyatkin},
  journal={Journal of Automata, Languages and Combinatorics},
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) ∈ E for each x 6= y. If W is k-uniform (each letter of W occurs exactly k times in it) then G is called k-representable. Examples of non-representable graphs are found in this paper. Some wide classes of graphs are proven to be 2and 3-representable. Several open problems are stated.