  Lexicographic Depth First Search (LexDFS) is a special variant of a Depth
First Search (DFS), which was introduced by Corneil and Krueger in 2008. While
this search has been used in various applications, in contrast to other graph
searches, no general linear time implementation is known to date. In 2014,
K\"ohler and Mouatadid achieved linear running time to compute some special
LexDFS orders for cocomparability graphs. In this paper, we present a linear
time implementation of LexDFS for chordal graphs. Our algorithm is able to find
any LexDFS order for this graph class. To the best of our knowledge this is the
first unrestricted linear time implementation of LexDFS on a non-trivial graph
class. In the algorithm we use a search tree computed by Lexicographic Breadth
First Search (LexBFS).
