Multitrees in random graphs
Alan Frieze, Wesley Pegden

TL;DR
This paper investigates the emergence of MultiTrees in random graphs, establishing thresholds for their existence and providing bounds for different numbers of spanning trees.
Contribution
It introduces the concept of MultiTrees in random graphs and determines the minimum size needed for their likely appearance.
Findings
Hitting time result for s=2 MultiTrees
O(n log n) bound for s≥3 MultiTrees
Thresholds for MultiTree existence in random graphs
Abstract
Let and . Let be independent permutations of the edges of the complete graph . A {\em MultiTree} is a set such that the edge sets induce spanning trees for . In this paper we study the following question: what is the smallest such that w.h.p. contains a MultiTree. We prove a hitting time result for and an bound for .
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Graph Theory Research · Finite Group Theory Research
