{
  "id": "1805.07425",
  "version": "v1",
  "published": "2018-05-16T15:21:43.000Z",
  "updated": "2018-05-16T15:21:43.000Z",
  "title": "Combinatorial Properties of Metrically Homogeneous Graphs",
  "authors": [
    "Matěj Konečný"
  ],
  "comment": "An unofficial version of author's Bachelor thesis",
  "categories": [
    "math.CO",
    "cs.DM",
    "math.LO"
  ],
  "abstract": "Ramsey theory looks for regularities in large objects. Model theory studies algebraic structures as models of theories. The structural Ramsey theory combines these two fields and is concerned with Ramsey-type questions about certain model-theoretic structures. In 2005, Ne\\v{s}et\\v{r}il initiated a systematic study of the so-called Ramsey classes of finite structures. This thesis is a contribution to the programme; we find Ramsey expansions of the primitive 3-constrained classes from Cherlin's catalogue of metrically homogeneous graphs. A key ingradient is an explicit combinatorial algorithm to fill-in the missing distances in edge-labelled graphs to obtain structures from Cherlin's classes. This algorithm also implies the extension property for partial automorphisms (EPPA), another combinatorial property of classes of finite structures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-16T15:21:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "metrically homogeneous graphs",
      "combinatorial property",
      "model theory studies algebraic structures",
      "finite structures",
      "ramsey theory looks"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}