On rainbow Tur\'{a}n Densities of Trees
Seonghyuk Im, Jaehoon Kim, Hyunwoo Lee, Haesong Seo

TL;DR
This paper investigates the maximum density of edge-colored graph systems avoiding rainbow trees, proving the algebraic nature of the rainbow Turán density for trees and characterizing extremal configurations.
Contribution
It introduces the concept of rainbow Turán density for trees, proves its algebraic property, and characterizes extremal graph structures and edge density thresholds.
Findings
Rainbow Turán density of trees is algebraic.
Characterization of extremal graph structures for rainbow trees.
Identification of edge density thresholds ensuring rainbow trees appear.
Abstract
For a given collection of graphs on a common vertex set , which we call a \emph{graph system}, a graph on a vertex set is called a \emph{rainbow subgraph} of if there exists an injective function such that for each . The maximum value of over -vertex graph systems having no rainbow subgraph isomorphic to is called the rainbow Tur\'{a}n number of . In this article, we study the rainbow Tur\'{a}n density of a tree . While the classical Tur\'{a}n density of a graph lies in the set , the rainbow Tur\'{a}n density exhibits different…
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Taxonomy
TopicsGraph theory and applications · Advanced Graph Theory Research · Limits and Structures in Graph Theory
