Spectral Perspectives on FAT Graph Colorings
Lies Beers, Raffaella Mulas
TL;DR
This paper explores FAT graph colorings, focusing on spectral methods to determine the FAT chromatic number for complete multipartite graphs and analyzing coloring behavior under various graph operations.
Contribution
It introduces spectral techniques to analyze FAT colorings and provides exact FAT chromatic numbers for all complete multipartite graphs.
Findings
Determined the FAT chromatic number for all complete multipartite graphs.
Analyzed the impact of graph operations on FAT colorings.
Combined spectral and combinatorial methods for results.
Abstract
We investigate Fair and Tolerant (FAT) graph colorings, a coloring framework in which each vertex is allowed to share its color with a prescribed fraction of its neighbors, while the remaining neighbors are required to be distributed evenly among the other coloring classes. In particular, we determine the FAT chromatic number for all complete multipartite graphs, and we analyze the behavior of FAT colorings under several graph operations. Although spectral methods form the primary focus, several combinatorial arguments are included to complement the results.
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