Graph Isomorphism Completeness for Trapezoid Graphs

Graph Isomorphism Completeness for Trapezoid Graphs

The complexity of the graph isomorphism problem for trapezoid graphs has been open over a decade. This paper shows that the problem is GI-complete. More precisely, we show that the graph isomorphism problem is GI-complete for comparability graphs of partially ordered sets with interval dimension 2 and height 3. In contrast, the problem is known to be solvable in polynomial time for comparabilit...

Completeness results for graph isomorphism

Graph isomorphism completeness for chordal bipartite graphs and strongly chordal graphs

This paper deals with the graph isomorphism (GI) problem for two graph classes: chordal bipartite graphs and strongly chordal graphs. It is known that GI problem is GI complete even for some special graph classes including regular graphs, bipartite graphs, chordal graphs, comparability graphs, split graphs, and k-trees with unbounded k. On the other side, the relative complexity of the GI probl...

Graph Isomorphism Completeness for Perfect Graphs and Subclasses of Perfect Graphs

A problem is said to be GI-complete if it is provably as hard as graph isomorphism; that is, there is a polynomial-time Turing reduction from the graph isomorphism problem. It is known that the GI problem is GI-complete for some special graph classes including regular graphs, bipartite graphs, chordal graphs and split graphs. In this paper, we prove that deciding isomorphism of double split gra...

Graph-Theoretic Algorithms Project Report Trapezoid Graphs

Trapezoid graphs are intersection graphs of trapezoids between two horizontal lines. They generalize both interval graphs and permutation graphs. Interval graphs are intersection graphs of intervals on the real line. Permutation graphs are intersection graphs of straight lines between two horizontal lines. They can be represented by a permutation diagram consisting of a pair of horizontal lines...