A k-path power is the k-power graph of a simple path of arbitrary length. Path powers form a
non-trivial subclass of proper interval graphs. Their clique-width is not bounded by a
constant, and no polynomial-time algorithm is known for computing their clique-width or
linear clique-width. We show that k-path powers above a certain size have linear clique-
width exactly k+ 2, providing the first complete characterisation of the linear clique-width of a
graph class of unbounded clique-width. Our characterisation results in a simple linear-time …

… Title: A Complete Characterisation of the Linear Clique-Width of Path Powers … Show
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