Rainbow spanning trees in randomly coloured $G_{k-out}$

TL;DR

This paper studies the existence of rainbow spanning trees in randomly coloured $G_{k-out}$ graphs, exploring how random edge colourings influence the formation of such trees.

Contribution

It introduces an analysis of rainbow spanning trees specifically within the context of randomly coloured $G_{k-out}$ graphs, a novel focus in graph theory.

Findings

Conditions for rainbow spanning trees in $G_{k-out}$ graphs

Impact of random edge colourings on spanning tree formation

Probabilistic thresholds for rainbow trees

Abstract

Given a graph $G=(V,E)$ on $n$ vertices and an assignment of colours to its edges, a set of edges $S \subseteq E$ is said to be rainbow if edges from $S$ have pairwise different colours assigned to them. In this paper, we investigate rainbow spanning trees in randomly coloured random $G_{k-out}$ graphs.