{
  "id": "2412.13945",
  "version": "v1",
  "published": "2024-12-18T15:27:53.000Z",
  "updated": "2024-12-18T15:27:53.000Z",
  "title": "Restricted subgraphs of edge-colored graphs and applications",
  "authors": [
    "Benny Sudakov"
  ],
  "comment": "This survey article is based on the talk which the author gave at European Congress of Mathematics 2024 in Sevilla. Comments are welcome",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "A properly edge-colored graph is a graph with a coloring of its edges such that no vertex is incident to two or more edges of the same color. A subgraph is called rainbow if all its edges have different colors. The problem of finding rainbow subgraphs or other restricted structures in edge-colored graphs has a long history, dating back to Euler's work on Latin squares. It has also proven to be a powerful method for studying several well-known questions in other areas. In this survey, we will provide a brief introduction to this topic, discuss several results in this area, and demonstrate their applications to problems in graph decomposition, additive combinatorics, theoretical computer science, and coding theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-18T15:27:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "edge-colored graph",
      "restricted subgraphs",
      "applications",
      "finding rainbow subgraphs",
      "eulers work"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}