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

Voir la notice de l'article dans European Digital Mathematics Library

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.
Classification : 05C60
Mots-clés : distinguishing, distinguishing number, list distinguishing, interval graph, list distinguishing number 
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Poppy Immel; Paul S. Wenger. The list Distinguishing Number Equals the Distinguishing Number for Interval Graphs. Discussiones Mathematicae Graph Theory, Tome 37 (2017) no. 1, p. 165. https://geodesic-test.mathdoc.fr/item/DMGT_2017__37_1_288067/