On List Coloring with Separation of the Complete Graph and Set System Intersections
Jean-Christophe Godin, R\'emi Grisot, Olivier Togni

TL;DR
This paper investigates the maximum intersection size in list coloring with separation for complete graphs, providing exact values for some parameters and bounds for others using advanced combinatorial techniques.
Contribution
It introduces an improved method based on set partitions to determine the separation number for complete graphs in list coloring with separation.
Findings
Exact separation numbers for certain parameters of complete graphs
Bounds established for remaining parameter ranges
Enhanced combinatorial techniques for list coloring problems
Abstract
We consider the following list coloring with separation problem: Given a graph and integers , find the largest integer such that for any list assignment of with for any vertex and for any edge of , there exists an assignment of sets of integers to the vertices of such that and for any vertex and for any edge . Such a value of is called the separation number of . Using a special partition of a set of lists for which we obtain an improved version of Poincar\'e's crible, we determine the separation number of the complete graph for some values of and , and prove bounds for the remaining values.
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Taxonomy
Topicsgraph theory and CDMA systems · Graph Labeling and Dimension Problems · Advanced Graph Theory Research
