Rainbow induced subgraphs in proper vertex colorings
Andrzej Kisielewicz, Marek Szyku{\l}a

TL;DR
This paper investigates the minimum size of graphs that guarantee rainbow induced subgraphs of a given graph in any proper coloring, providing bounds, exact values for certain classes, and exploring related combinatorial problems.
Contribution
It introduces bounds and exact values for the rainbow subgraph parameter (H), advancing understanding of rainbow structures in proper colorings and their computational aspects.
Findings
Established bounds for (H)
Computed exact values for specific graph classes
Explored combinatorial problems related to paths
Abstract
For a given graph we define to be the minimum order of a graph such that every proper vertex coloring of contains a rainbow induced subgraph isomorphic to . We give upper and lower bounds for , compute the exact value for some classes of graphs, and consider an interesting combinatorial problem connected with computation of for paths. This research is motivated by some ideas in on-line graph coloring algorithms.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Graph Theory Research · Graph Labeling and Dimension Problems
