Tolerance graphs and orders [chapter]

Stefan Felsner
1993 Lecture Notes in Computer Science  
We show that if a tolerance graph is the complement of a comparability graph it is a trapezoid graph, i.e., the complement of an order of interval dimension at most 2. As consequences we are able to give obstructions for the class of bounded tolerance graphs and to give an example of a graph which is alternatingly orientable but not a tolerance graph. We also characterize the tolerance graphs among complements of trees
doi:10.1007/3-540-56402-0_32 fatcat:7f7x2wat45ccxjpn7fffkf4zwi