This paper explores the mixing time of the random transposition walk on the symmetric group Sn. While it has long been known that this walk mixes in O(n log n) time, this result has not previously been attained using coupling. A coupling argument showing the correct order mixing time is presented. This is accomplished by first projecting to conjugacy classes, and then using the Bubley-Dyer path...

Bipartite permutation graphs have several nice characterizations in terms of vertex ordering. Besides, as AT-free graphs, they have a linear structure in the sense that any connected bipartite permutation graph has a dominating path. In the present paper, we elaborate the linear structure of bipartite permutation graphs by showing that any connected graph in the class can be stretched into a "p...