Rainbow independent sets in certain classes of graphs
Ron Aharoni, Joseph Briggs, Jinha Kim, Minki Kim

TL;DR
This paper investigates the minimal number of independent sets needed to guarantee a rainbow independent subset of a certain size within various graph classes, extending known results beyond line graphs.
Contribution
It introduces and analyzes the function $f_ ext{class}(n,m)$ for different graph classes, broadening understanding of rainbow independent sets in graph theory.
Findings
Determined bounds for $f_ ext{class}(n,m)$ in specific graph classes
Extended known results from line graphs to other classes
Provided conditions for the finiteness of $f_ ext{class}(n,m)$
Abstract
For a given class of graphs and given integers , let be the minimal number such that every independent -sets in any graph belonging to have a (possibly partial) rainbow independent -set. Motivated by known results on the finiteness and actual value of when is the class of line graphs of graphs, we study this function for various other classes.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Graph Theory Research · semigroups and automata theory
