On representable graphs

Authors:
Sergey Kitaev;Artem Pyatkin
Affiliations:
Reykjavík University, Reykjaví Iceland;Sobolev Institute of Mathematics, Novosibirsk, Russia
Venue:
Journal of Automata, Languages and Combinatorics
Year:
2008

Citing 1
Cited 3

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Abstract

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 ≠ y. If W is k-uniform (each letter of W occurs exactly k times in it) then G is called k-representable. We prove that a graph is representable if and only if it is k-representable for some k. Examples of non-representable graphs are found in this paper. Some wide classes of graphs are proven to be 2- and 3-representable. Several open problems are stated.