Upper bounds for the list-distinguishing chromatic number
Amitayu Banerjee, Zal\'an Moln\'ar, Alexa Gopaulsingh
TL;DR
This paper establishes new upper bounds for the list-distinguishing chromatic number of graphs, extending Brooks' Theorem analogs and analyzing specific graph families to deepen understanding of graph coloring constraints.
Contribution
It introduces new bounds for the list-distinguishing chromatic number based on coloring and list-chromatic numbers, and computes this number for various graph families.
Findings
Established Brooks' Theorem analogs for list-distinguishing chromatic number.
Derived upper bounds in terms of coloring number and list-chromatic number.
Determined list-distinguishing chromatic number for specific graph families like book graphs.
Abstract
We prove analogs of Brooks' Theorem for the list-distinguishing chromatic number of different classes of simple finite connected graphs. Moreover, we determine two upper bounds for the list-distinguishing chromatic number of a graph G in terms of the coloring number of G and the list-chromatic number of G. We also determine the list-distinguishing chromatic number for various families of graphs (for example: the book graphs).
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Taxonomy
TopicsGraph Labeling and Dimension Problems