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How many randomly colored edges make a randomly colored dense graph\n rainbow hamiltonian or rainbow connected?

2018/02/01 by Michael Anastos, Alan Frieze, Anastos, Michael +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.1802.00433

openalex publication_date 2018/02/01 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

In this paper we study the randomly edge colored graph that is obtained by\nadding randomly colored random edges to an arbitrary randomly edge colored\ndense graph. In particular we ask how many colors and how many random edges are\nneeded so that the resultant graph contains a fixed number of edge disjoint\nrainbow Hamilton cycles. We also ask when in the resultant graph every pair of\nvertices is connected by a rainbow path.\n

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