TL;DR
This paper establishes threshold results for rainbow structures in random graphs with edges randomly colored, resolving a recent problem and strengthening previous results in the field.
Contribution
It extends existing threshold results to the rainbow setting and applies these to rainbow structures in randomly edge-colored graphs.
Findings
Established the threshold for rainbow structures in random graphs.
Strengthened previous threshold results by Spiro.
Applied results to rainbow structures in randomly colored graphs.
Abstract
Resolving a recent problem of Bell, Frieze, and Marbach, we establish both the threshold result of Frankston--Kahn--Narayanan--Park, and its strengthening by Spiro, in the rainbow setting. This has applications to the thresholds for rainbow structures in random graphs where each edge is given a uniformly random color from a set of given colors.
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Taxonomy
TopicsDigital Image Processing Techniques · Constraint Satisfaction and Optimization · Advanced Topology and Set Theory