Word-representability of triangulations of grid-covered cylinder graphs

摘要

A graph G = (V, E) is word-representable if there exists a word w over the alphabet V such that letters x and y, x not equal y, alternate in w if and only if (x, y) is an element of E. Halldorsson, Kitaev and Pyatkin have shown that a graph is word-representable if and only if it admits a so-called semi-transitive orientation. A corollary of this result is that any 3-colorable graph is word-representable.