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This paper examines the class ofbipartite permutation graphs. Two chaiacterizations of graphs i n this class are presented. These characterizations l ead to a linear time recognition algorithm, and to polynomial time algorithms for a number of NP-complete problems when restricted to graphs i n this class. Bipartite graphs and permutation graphs are two well… (More)

An independent set of three vertices such that each pair is joined by a path that avoids the neighborhood of the third is called an asteroidal triple. A graph is asteroidal triple-free (AT-free, for short) if it contains no asteroidal triples. The motivation for this investigation was provided, in part, by the fact that the asteroidal triple-free graphs… (More)

A graph is an interval graph if it is the intersection graph of intervals on a line. Interval graphs are known to be the intersection of chordal graphs and asteroidal triple-free graphs, two families where the well-known Lexicographic Breadth First Search (LBFS) plays an important algorithmic and structural role. In this paper we show that interval graphs… (More)

An independent set of three of vertices is called an asteroidal triple if between each pair in the triple there exists a path that avoids the neighbourhood of the third. A graph is asteroidal triple-free (AT-free, for short) if it contains no asteroidal triple. The motivation for this work is provided, in part, by the fact that AT-free graphs ooer a common… (More)

An independent set of three vertices is called an asteroidal triple if between every two vertices in the triple there exists a path avoiding the neighbourhood of the third. A graph is asteroidal triple-free (AT-free, for short) if it contains no asteroidal triple. A classic result states that a graph is an interval graph if and only if it is chordal and… (More)

An independent set fx; y; zg is called an asteroidal triple if between any pair in the triple there exists a path that avoids the neighborhood of the third. A graph is referred to as AT-free if it does not contain an asteroidal triple. We present a simple linear-time algorithm to compute a dominating path in a connected AT-free graph.