Distinguishing locally finite trees

Hannah Schreiber, Svenja Hüning, Judith Kloas, Wilfried Imrich, Thomas Tucker

Research output: Contribution to journalArticleResearchpeer-review

Abstract

The distinguishing number D(G) of a graph G is the smallest number of colors that is needed to color the vertices of G such that the only color preserving automorphism is the identity. For infinite graphs D(G) is bounded by the supremum of the valences, and for finite graphs by Δ(G)+1, where Δ(G) is the maximum valence. Given a finite or infinite tree T of bounded finite valence k and an integer c, where 2≤c≤k, we are interested in coloring the vertices of T by c colors, such that every color preserving automorphism fixes as many vertices as possible. In this sense we show that there always exists a c-coloring for which all vertices whose distance from the next leaf is at least ⌈logck⌉ are fixed by any color preserving automorphism, and that one can do much better in many cases.
Original languageEnglish
JournalThe Australasian Journal of Combinatorics
Publication statusSubmitted - 2018

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Automorphism
Colouring
Infinite Graphs
Finite Graph
Supremum
Color
Leaves
Integer
Graph in graph theory

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Schreiber, H., Hüning, S., Kloas, J., Imrich, W., & Tucker, T. (2018). Distinguishing locally finite trees. Manuscript submitted for publication.

Distinguishing locally finite trees. / Schreiber, Hannah; Hüning, Svenja; Kloas, Judith; Imrich, Wilfried; Tucker, Thomas.

In: The Australasian Journal of Combinatorics, 2018.

Research output: Contribution to journalArticleResearchpeer-review

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