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Discrete Math."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>A subgraph $H$ of a graph $G$ is isometric if the distances between vertices in $H$ coincide with the distances between the corresponding vertices in $G$. We show that for any integer $n\\ge 1$, there is a graph on $3^{n+O(\\log^2 n)}$ vertices that contains isometric copies of all $n$-vertex graphs. Our main tool is a new type of distance labelling scheme, whose study might be of independent interest.<\/jats:p>","DOI":"10.1137\/21m1406155","type":"journal-article","created":{"date-parts":[[2021,6,8]],"date-time":"2021-06-08T15:28:44Z","timestamp":1623166124000},"page":"1224-1237","source":"Crossref","is-referenced-by-count":2,"title":["Isometric Universal Graphs"],"prefix":"10.1137","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6200-0514","authenticated-orcid":true,"given":"Louis","family":"Esperet","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cyril","family":"Gavoille","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Carla","family":"Groenland","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,6,8]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/s00039-017-0396-9"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-1990-1065053-0"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/S0895480103433409"},{"key":"atypb4","unstructured":"S. Alstrup, S. Dahlgaard, M. B. T. Knudsen, and E. Porat,\n                      Sublinear distance labeling\n                      , in Proceedings of the 24th Annual European Symposium on Algorithms, ESA 2016, Aarhus, Denmark, 2016, P. Sankowski and C. D. Zaroliagis, eds., LIPIcs 57, Schloss Dagstuhl-Leibniz-Zentrum f\u00fcr Informatik, 2016, pp. 5:1-5:15,https:\/\/doi.org\/10.4230\/LIPIcs.ESA.2016.5."},{"key":"atypb5","first-page":"338","author":"Alstrup S.","year":"2016","journal-title":"Philadelphia"},{"key":"atypb6","unstructured":"S. Alstrup, I. L. G\u00f8rtz, E. B. Halvorsen, and E. Porat,\n                      Distance labeling schemes for trees\n                      , in Proceedings of the 43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016, Rome, Italy, 2016, I. Chatzigiannakis, M. Mitzenmacher, Y. Rabani, and D. Sangiorgi, eds., LIPIcs 55, Schloss Dagstuhl-Leibniz-Zentrum f\u00fcr Informatik, 2016, pp. 132:1-132:16,https:\/\/doi.org\/10.4230\/LIPIcs.ICALP.2016.132."},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1137\/16M1105967"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/S0195-6698(81)80015-7"},{"key":"atypb9","doi-asserted-by":"crossref","unstructured":"M. Bonamy, L. Esperet, C. Groenland, and A. Scott,\n                      Optimal Labelling Schemes for Adjacency, Comparability and Reachability\n                      , preprint,http:\/\/arxiv.org\/abs\/2012.01764, 2020.","DOI":"10.1145\/3406325.3451102"},{"key":"atypb10","first-page":"446","author":"Bonamy M.","year":"2020","journal-title":"Philadelphia"},{"key":"atypb11","first-page":"17","author":"F. R.","year":"1990","journal-title":"Berlin"},{"key":"atypb12","first-page":"265","author":"Chung F. R. K.","year":"1981","journal-title":"New York"},{"key":"atypb13","doi-asserted-by":"crossref","unstructured":"V. Dujmovi\u0107, L. Esperet, C. Gavoille, G. Joret, P. Micek, and P. Morin,\n                      Adjacency labelling for planar graphs (and beyond)\n                      , in Proceedings of the 61th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2020, virtual conference, 2020.","DOI":"10.1109\/FOCS46700.2020.00060"},{"key":"atypb14","doi-asserted-by":"crossref","unstructured":"O. Freedman, P. Gawrychowski, P. K. Nicholson, and O. Weimann,\n                      Optimal distance labeling schemes for trees\n                      , in Proceedings of the 36th Annual ACM Symposium on Principles of Distributed Computing (PODC), ACM Press, 2017, pp. 185-194,https:\/\/doi.org\/10.1145\/3087801.3087804.","DOI":"10.1145\/3087801.3087804"},{"key":"atypb15","first-page":"582","author":"Gavoille C.","year":"2007","journal-title":"Israel"},{"key":"atypb16","unstructured":"C. Gavoille and C. Paul,\n                      Small Universal Distance Matrices\n                      , Research Report RR-1290-03, Laboratoire Bordelais de Recherche en Informatique, Talence, France, 2003."},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgor.2004.05.002"},{"key":"atypb18","doi-asserted-by":"crossref","unstructured":"P. Gawrychowski, A. Kosowski, and P. Uzna\u0144ski,\n                      Sublinear-space distance labeling using hubs\n                      , in Distributed Computing, C. Gavoille and D. 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