Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorial Properties of Metrically Homogeneous Graphs   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.

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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio