Abstract
Let G be a connected graph of n vertices and m edges. The problem of finding a depth-first spanning tree of G is to find a subgraph of G connecting the n vertices with n − 1 edges by depth-first search. In this paper, we propose an O( n) time algorithm for solving this problem on trapezoid graphs. Our algorithm can also find depth-first spanning trees of permutation graphs in linear time, improving the recent algorithm on permutation graphs which takes O( n log log n) time.
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