{"id":434,"date":"2026-03-31T10:00:26","date_gmt":"2026-03-31T08:00:26","guid":{"rendered":"https:\/\/web.umons.ac.be\/fs-informatique\/?p=434"},"modified":"2026-03-31T10:00:26","modified_gmt":"2026-03-31T08:00:26","slug":"the-algorithms-lab-launches-the-new-phoeg-web-interface-for-research-and-education-in-graph-theory","status":"publish","type":"post","link":"https:\/\/web.umons.ac.be\/fs-informatique\/en\/2026\/03\/31\/the-algorithms-lab-launches-the-new-phoeg-web-interface-for-research-and-education-in-graph-theory\/","title":{"rendered":"The Algorithms Lab launches the new PHOEG web interface for Research and Education in Graph Theory"},"content":{"rendered":"<p data-path-to-node=\"3\"><span data-path-to-node=\"3,1\"><span class=\"citation-84\"><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-429 alignleft\" src=\"https:\/\/web.umons.ac.be\/app\/uploads\/sites\/209\/2026\/03\/Capture-decran-2026-03-31-a-09.50.42-300x170.png\" alt=\"\" width=\"192\" height=\"109\" \/>The Algorithms Lab is proud to announce the release of a completely redesigned web interface for PHOEG (PHOEG Helps to Obtain Extremal Graphs), an interactive online tool designed to assist researchers and educators in graph theory<\/span><\/span><span data-path-to-node=\"3,3\">. This release coincides with the submission of our latest preprint detailing the platform&rsquo;s architecture and applications.<\/span><\/p>\n<p data-path-to-node=\"4\"><span data-path-to-node=\"4,0\"><b data-path-to-node=\"4,0\" data-index-in-node=\"0\">An Exact Geometrical Approach<\/b> <\/span><span data-path-to-node=\"4,2\"><span class=\"citation-83\">Unlike tools that rely on heuristic or probabilistic methods, PHOEG commits to an exact geometrical approach<\/span><\/span><span data-path-to-node=\"4,4\">. <\/span><span data-path-to-node=\"4,6\"><span class=\"citation-82\">It embeds graphs into a two-dimensional invariant space and computes their convex hull<\/span><\/span><span data-path-to-node=\"4,8\">. <\/span><span data-path-to-node=\"4,10\"><span class=\"citation-81\">In this mathematical space, the facets of the resulting polytope represent linear inequalities between the chosen invariants, while the vertices correspond to the extremal graphs<\/span><\/span><span data-path-to-node=\"4,12\">.<\/span><\/p>\n<p data-path-to-node=\"5\"><span data-path-to-node=\"5,0\"><b data-path-to-node=\"5,0\" data-index-in-node=\"0\"><img loading=\"lazy\" decoding=\"async\" class=\"alignright  wp-image-430\" src=\"https:\/\/web.umons.ac.be\/app\/uploads\/sites\/209\/2026\/03\/phoeg_example-300x165.png\" alt=\"\" width=\"409\" height=\"225\" srcset=\"https:\/\/web.umons.ac.be\/app\/uploads\/sites\/209\/2026\/03\/phoeg_example-300x165.png 300w, https:\/\/web.umons.ac.be\/app\/uploads\/sites\/209\/2026\/03\/phoeg_example-1024x564.png 1024w, https:\/\/web.umons.ac.be\/app\/uploads\/sites\/209\/2026\/03\/phoeg_example-768x423.png 768w, https:\/\/web.umons.ac.be\/app\/uploads\/sites\/209\/2026\/03\/phoeg_example-1536x846.png 1536w, https:\/\/web.umons.ac.be\/app\/uploads\/sites\/209\/2026\/03\/phoeg_example-2048x1128.png 2048w, https:\/\/web.umons.ac.be\/app\/uploads\/sites\/209\/2026\/03\/phoeg_example-1198x660.png 1198w, https:\/\/web.umons.ac.be\/app\/uploads\/sites\/209\/2026\/03\/phoeg_example-30x17.png 30w, https:\/\/web.umons.ac.be\/app\/uploads\/sites\/209\/2026\/03\/phoeg_example-60x33.png 60w, https:\/\/web.umons.ac.be\/app\/uploads\/sites\/209\/2026\/03\/phoeg_example-360x198.png 360w\" sizes=\"auto, (max-width: 409px) 100vw, 409px\" \/>What&rsquo;s new in this version?<\/b> <\/span><span data-path-to-node=\"5,2\"><span class=\"citation-80\">The new platform provides seamless access to a massive database of approximately 34 million pairwise non-isomorphic graphs, encompassing all graphs up to order 10<\/span><\/span><span data-path-to-node=\"5,4\">.<\/span><\/p>\n<ul data-path-to-node=\"6\">\n<li>\n<p data-path-to-node=\"6,0,1\"><span data-path-to-node=\"6,0,1,0\"><b data-path-to-node=\"6,0,1,0\" data-index-in-node=\"0\"><span class=\"citation-79\">For researchers:<\/span><\/b><span class=\"citation-79\"> The interface allows for complex explorations using numerical constraints, colorations, and highlighting<\/span><\/span><span data-path-to-node=\"6,0,1,2\">. <\/span><span data-path-to-node=\"6,0,1,4\"><span class=\"citation-78\">It acts as a powerful catalyst for forming new mathematical conjectures, finding counterexamples, and building structural intuition<\/span><\/span><span data-path-to-node=\"6,0,1,6\">. <\/span><span data-path-to-node=\"6,0,1,8\"><span class=\"citation-77\">Additionally, a standalone RESTful API is now available for automated, programmatic access to the database<\/span><\/span><span data-path-to-node=\"6,0,1,10\">.<\/span><\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"6,1,1\"><span data-path-to-node=\"6,1,1,0\"><b data-path-to-node=\"6,1,1,0\" data-index-in-node=\"0\"><span class=\"citation-76\">For educators:<\/span><\/b><span class=\"citation-76\"> The platform features a comprehensive suite of built-in interactive tutorials<\/span><\/span><span data-path-to-node=\"6,1,1,2\">. <\/span><span data-path-to-node=\"6,1,1,4\"><span class=\"citation-75\">It is already being actively used in advanced graph theory courses at the University of Mons and Polytechnique Montr\u00e9al to help students empirically rediscover classical theorems<\/span><\/span><span data-path-to-node=\"6,1,1,6\">.<\/span><\/p>\n<\/li>\n<\/ul>\n<p data-path-to-node=\"7\"><b data-path-to-node=\"7\" data-index-in-node=\"0\">Explore the tool and the research:<\/b><\/p>\n<ul data-path-to-node=\"8\">\n<li>\n<p data-path-to-node=\"8,0,0\"><span data-path-to-node=\"8,0,0,1\"><span class=\"citation-74\">\ud83c\udf10 <\/span><b data-path-to-node=\"8,0,0,1\" data-index-in-node=\"3\"><span class=\"citation-74\">Try the web interface:<\/span><\/b> <a class=\"ng-star-inserted\" href=\"https:\/\/phoeg.umons.ac.be\" target=\"_blank\" rel=\"noopener\" data-hveid=\"0\" data-ved=\"0CAAQ_4QMahgKEwjJoeOCycmTAxUAAAAAHQAAAAAQ3gI\"><span class=\"citation-74\">https:\/\/phoeg.umons.ac.be<\/span><\/a> <\/span><\/p>\n<\/li>\n<li>\n<p data-path-to-node=\"8,1,0\">\ud83d\udcc4 <b data-path-to-node=\"8,1,0\" data-index-in-node=\"3\">Read the preprint on arXiv:<\/b> <a class=\"ng-star-inserted\" href=\"https:\/\/www.google.com\/search?q=https:\/\/arxiv.org\/abs\/2603.27242&amp;authuser=1\" target=\"_blank\" rel=\"noopener\" data-hveid=\"0\" data-ved=\"0CAAQ_4QMahgKEwjJoeOCycmTAxUAAAAAHQAAAAAQ3wI\">https:\/\/arxiv.org\/abs\/2603.27242<\/a><\/p>\n<\/li>\n<\/ul>\n<p id=\"p-rc_1d4f0599b8843385-49\" data-path-to-node=\"10\"><span data-path-to-node=\"10,0\"><i data-path-to-node=\"10,0\" data-index-in-node=\"0\"><span class=\"citation-73\">Authors: S\u00e9bastien Bonte, Gauvain Devillez, Valentin Dusollier, and Hadrien M\u00e9lot.<\/span><\/i><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Algorithms Lab unveils the new PHOEG web interface, an interactive platform dedicated to extremal graph theory. Released alongside a new scientific preprint, this major update opens access to a database of over 34 million graphs to facilitate conjecture discovery and education.<\/p>\n","protected":false},"author":130,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[52,50,48],"tags":[],"class_list":["post-434","post","type-post","status-publish","format-standard","hentry","category-education","category-publication","category-research-tools"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>The Algorithms Lab launches the new PHOEG web interface for Research and Education in Graph Theory - FS - D\u00e9partement d&#039;Informatique<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/web.umons.ac.be\/fs-informatique\/en\/2026\/03\/31\/the-algorithms-lab-launches-the-new-phoeg-web-interface-for-research-and-education-in-graph-theory\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The Algorithms Lab launches the new PHOEG web interface for Research and Education in Graph Theory - FS - D\u00e9partement d&#039;Informatique\" \/>\n<meta property=\"og:description\" content=\"The Algorithms Lab unveils the new PHOEG web interface, an interactive platform dedicated to extremal graph theory. 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