[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-154278-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-154278-en":131},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","graph-theory-2025-report-no-1","Graph Theory - 2025 Report No. 1","","Graph theory workshop report summarizing recent major developments, with an emphasis on twin-width and hereditary properties of graphs and their fast-evolving results. The program combined broad coverage across graph theory with two central themes, plus focused talks on additional advances such as Erdős–Hajnal conjecture, Erdos–Pósa properties, and related structural techniques. The report also documents the hybrid format and highlights opportunities for collaboration, including active involvement of early career researchers.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & Report",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/graph-theory-2025-report-no-1/154278/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/graph-theory-2025-report-no-1/154278.png","ImageObject",300,407,{"name":42,"@type":43},"Olivia Brown","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-17","2026-08-28",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",13,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What were the main focus areas of the Graph Theory workshop?","Question",{"text":63,"@type":64},"The workshop primarily focused on results about twin-width and hereditary properties of graphs, alongside presentations addressing other recent developments in graph theory.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How was the workshop conducted and who participated?",{"text":68,"@type":64},"It used a hybrid format with 44 participants on-site and 4 online. The report notes that several online participants could not attend due to parenting, visa, or health reasons.",{"name":70,"@type":61,"acceptedAnswer":71},"What does the report highlight about the workshop program structure?",{"text":72,"@type":64},"Each of the five days began with a 50-minute overview talk and a 10-minute discussion, with additional short talks, minipresentations, collaboration time, and a traditional workshop trip.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},154278,1787890396,{"code":4,"msg":82,"data":83},"success",[84,88,92,96,101,106,111,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":93,"show_sort_weight":94,"slug":95},"Exam",70,"exam",{"id":97,"doc_module":4,"doc_module_name":25,"category_name":98,"show_sort_weight":99,"slug":100},5,"Comic",60,"comic",{"id":102,"doc_module":4,"doc_module_name":25,"category_name":103,"show_sort_weight":104,"slug":105},6,"Technology",50,"technology",{"id":107,"doc_module":4,"doc_module_name":25,"category_name":108,"show_sort_weight":109,"slug":110},7,"Healthcare",40,"healthcare",{"id":112,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":113,"slug":114},8,30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":97,"slug":130},19,"General","general",{"code":4,"msg":82,"data":132},{"doc_id":79,"user_id":133,"nickname":42,"user_avatar":134,"doc_module":4,"category_id":112,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":94,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":80,"read_time":144,"preview_page_count":4},16904993612988,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Mathematisches Forschungsinstitut Oberwolfach  \nReport No. 1/2025  \nDOI: 10.4171/OWR/2025/1  \nGraph Theory  \nOrganized by  \nVida Dujmovic, Ottawa  \nDan Kr´al’, Brno  \nAlex Scott, Oxford  \n5 January – 10 January 2025  \nAbstract. The workshop provided a venue for discussing several recent major developments in graph theory, with a primary focus on results concerning the notion of twin-width and hereditary properties of graphs. Both areas have seen a very rapid development recently, as reflected in the many results presented during the workshop. In addition to many interesting talks spanning the whole breadth of graph theory, the workshop also offered valuable  \ncollaboration opportunities, which also engaged early career researchers.  \nMathematics Subject Classi􀀌cation (2020): 05Cxx.  \nLicense: Unless otherwise noted, the content of this report is licensed under CC BY SA 4.0 .  \nIntroduction by the Organizers  \nGraph theory has seen many significant results over the past three years. The workshop offered an opportunity for the community to meet and discuss the major recent developments. Talks covering two main themes of the workshop, hereditary properties of graphs and the notion of twin-width, were complemented by more focused talks highlighting recent advancements in other areas of graph theory.  \nThe workshop was attended by 44 participants on-site and 4 participants online. One on-line participant was unable to attend due to parenting responsibilities, one due to visa related issues and two due to health reasons. We are indebted to Oberwolfach Research Institute for making arrangements for the on-line attendance of these four participants, particularly for providing excellent technical facilities supporting the hybrid format of the workshop. We would also like to thank Marcin Bria´nski and Tung Nguyen for taking great care of the videoconferencing facilities throughout the entire workshop.  \n6 Oberwolfach Report 1/2025  \nThe workshop program started on Monday morning and concluded in the early afternoon on Friday. Each of the five days began with a 50-minute overview talk, followed by a 10-minute discussion. These talks were given by Maria Chudnovsky, Eun Jung Kim, Jacob Fox, Piotr Micek and Luke Postle. In particular, Maria Chudnovsky opened the theme of hereditary properties of graphs in her Monday talk, while Eun Jung Kim surveyed the notion of twin-width in her Tuesday talk. Most of the remaining program on Monday was devoted to 3-minute minipresentations that were given by each participant; the minipresentations were intended to introduce the participants and their research areas to one another. The full Monday program concluded with an open problem session designed to spark productive discussions for the rest of the week. The scientific program on the following days included 21 short talks, in addition to the 5 long talks given at the beginning of each day. A substantial part of the afternoon each day was left free for collaborative work while Wednesday afternoon was completely free for the traditional workshop trip. We were pleased that the workshop attendees included many early career researchers and females, and this diversity was also well reflected among those giving the talks.  \nThe two main themes were hereditary properties of graphs, i.e., those closed under taking induced subgraphs, and the notion of twin-width. Both themes have seen very major developments recently. On Monday, Maria Chudnovsky reported on her work on induced subgraph obstructions to bounded pathwidth (path and tree decompositions are powerful tools in structural and algorithmic graph theory with many applications) . Later in the week, Tung Nguyen updated the participants on his results on the Erd˝os–Hajnal conjecture, a major open problem concerning homogeneous subgraphs in hereditary classes of graphs, and Peter Nelson discussed the conjecture in the matroid setting.  \nThe survey talk by Eun Jung Kim in the morning on Tuesday kicked off the theme of","cbCaika1kwwtlCNv","https://ap.wps.com/l/cbCaika1kwwtlCNv","pdf",769944,"English","# Introduction by the Organizers\n## Workshop goals and themes\n## Participation and hybrid format\n# Workshop program and sessions\n## Daily schedule and talks\n## Minipresentations and open problems\n# Scientific themes and recent developments\n## Hereditary properties of graphs\n## Twin-width and related applications\n# Acknowledgement and closing notes","[{\"question\":\"What were the main focus areas of the Graph Theory workshop?\",\"answer\":\"The workshop primarily focused on results about twin-width and hereditary properties of graphs, alongside presentations addressing other recent developments in graph theory.\"},{\"question\":\"How was the workshop conducted and who participated?\",\"answer\":\"It used a hybrid format with 44 participants on-site and 4 online. The report notes that several online participants could not attend due to parenting, visa, or health reasons.\"},{\"question\":\"What does the report highlight about the workshop program structure?\",\"answer\":\"Each of the five days began with a 50-minute overview talk and a 10-minute discussion, with additional short talks, minipresentations, collaboration time, and a traditional workshop trip.\"}]","Graph Theory - 2025 Report No. 1 | PDF",176]