Ramsey properties of edge-labelled graphs via completions

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Jan Hubička Matěj Konečný Jaroslav Nešetřil


Motivated by applications in structural Ramsey theory, we describe “metric-like” classes of edge-labelled graphs, study their completion problems and find Ramsey expansions. They turn out to be general enough to incorporate most of the known Ramsey results for edge-labelled graphs under a common framework and also solve a problem of Conant on generalised metric spaces. As a corollary of understanding completions, one obtains homomorphism dualities for these classes.

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Hubička, J., Konečný, M., & Nešetřil, J. (2019). Ramsey properties of edge-labelled graphs via completions. Acta Mathematica Universitatis Comenianae, 88(3), 801-805. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1259/727