Document Type

Article

Publication Date

5-1-2016

Journal / Book Title

Random Structures & Algorithms

Abstract

Let HPn,m,k be drawn uniformly from all m-edge, k-uniform, k-partite hypergraphs where each part of the partition is a disjoint copy of [n]. We let HPn,m,k(κ) be an edge colored version, where we color each edge randomly from one of κ colors. We show that if κ=n and m=Knlogn where K is sufficiently large then w.h.p. there is a rainbow colored perfect matching. I.e. a perfect matching in which every edge has a different color. We also show that if n is even and m=Knlogn where K is sufficiently large then w.h.p. there is a rainbow colored Hamilton cycle in Gn,m(n). Here Gn,m(n) denotes a random edge coloring of Gn,m with n colors. When n is odd, our proof requires m=ω(nlogn) for there to be a rainbow Hamilton cycle.

DOI

10.1002/rsa.20594

Published Citation

Bal, D. and Frieze, A. (2016), Rainbow matchings and Hamilton cycles in random graphs†. Random Struct. Alg., 48: 503-523. https://doi.org/10.1002/rsa.20594

Download
Link to Publisher
Link at MSU

Share

COinS