Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
A recognition algorithm for II-graphs
A recognition algorithm for II-graphs
On the 2-chain subgraph cover and related problems
Journal of Algorithms
Proper and unit tolerance graphs
Discrete Applied Mathematics - Special volume: Aridam VI and VII, Rutcor, New Brunswick, NJ, USA (1991 and 1992)
On the structure of trapezoid graphs
Discrete Applied Mathematics
Modular decomposition and transitive orientation
Discrete Mathematics - Special issue on partial ordered sets
The Recognition of Tolerance and Bounded Tolerance Graphs
SIAM Journal on Computing
The recognition of triangle graphs
Theoretical Computer Science
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Trapezoid graphs are the intersection family of trapezoids where every trapezoid has a pair of opposite sides lying on two parallel lines. These graphs have received considerable attention and lie strictly between permutation graphs (where the trapezoids are lines) and cocomparability graphs (the complement has a transitive orientation). The operation of ''vertex splitting'', introduced in (Cheah and Corneil, 1996) [3], first augments a given graph G and then transforms the augmented graph by replacing each of the original graph's vertices by a pair of new vertices. This ''splitted graph'' is a permutation graph with special properties if and only if G is a trapezoid graph. Recently vertex splitting has been used to show that the recognition problems for both tolerance and bounded tolerance graphs is NP-complete (Mertzios et al., 2010) [11]. Unfortunately, the vertex splitting trapezoid graph recognition algorithm presented in (Cheah and Corneil, 1996) [3] is not correct. In this paper, we present a new way of augmenting the given graph and using vertex splitting such that the resulting algorithm is simpler and faster than the one reported in (Cheah and Corneil, 1996) [3].