Geodesic
The list Distinguishing Number Equals the Distinguishing Number for Interval Graphs
Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 1, pp. 165-174

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A distinguishing coloring of a graph G is a coloring of the vertices so that every nontrivial automorphism of G maps some vertex to a vertex with a different color. The distinguishing number of G is the minimum k such that G has a distinguishing coloring where each vertex is assigned a color from 1, . . ., k. A list assignment to G is an assignment L = L(v)v∈V (G) of lists of colors to the vertices of G. A distinguishing L-coloring of G is a distinguishing coloring of G where the color of each vertex v comes from L(v). The list distinguishing number of G is the minimum k such that every list assignment to G in which |L(v)| = k for all v ∈ V (G) yields a distinguishing L-coloring of G. We prove that if G is an interval graph, then its distinguishing number and list distinguishing number are equal.
Keywords: distinguishing, distinguishing number, list distinguishing, interval graph 
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     title = {The list {Distinguishing} {Number} {Equals} the {Distinguishing} {Number} for {Interval} {Graphs}},
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Immel, Poppy; Wenger, Paul S. The list Distinguishing Number Equals the Distinguishing Number for Interval Graphs. Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 1, pp. 165-174. http://geodesic.mathdoc.fr/item/DMGT_2017_37_1_a12/