BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Discrete Mathematics Group - ECPv6.15.20//NONSGML v1.0//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
X-ORIGINAL-URL:https://dimag.ibs.re.kr
X-WR-CALDESC:Events for Discrete Mathematics Group
REFRESH-INTERVAL;VALUE=DURATION:PT1H
X-Robots-Tag:noindex
X-PUBLISHED-TTL:PT1H
BEGIN:VTIMEZONE
TZID:Asia/Seoul
BEGIN:STANDARD
TZOFFSETFROM:+0900
TZOFFSETTO:+0900
TZNAME:KST
DTSTART:20190101T000000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20201203T163000
DTEND;TZID=Asia/Seoul:20201203T173000
DTSTAMP:20260424T000009
CREATED:20201013T135812Z
LAST-MODIFIED:20240705T194003Z
UID:3122-1607013000-1607016600@dimag.ibs.re.kr
SUMMARY:Deniz Sarikaya\, What means Hamiltonicity for infinite graphs and how to force it via forbidden induced subgraphs
DESCRIPTION:The study of Hamiltonian graphs\, i.e. finite graphs having a cycle that contains all vertices of the graph\, is a central theme of finite graph theory. For infinite graphs such a definition cannot work\, since cycles are finite. We shall debate possible concepts of Hamiltonicity for infinite graphs and eventually follow the topological approach by Diestel and Kühn [2\,3]\, which allows to generalize several results about being a Hamiltonian graph to locally finite graphs\, i.e. graphs where each vertex has finite degree. An infinite cycle of a locally finite connected graph G is defined as a homeomorphic image of the unit circle $S^1$  in the Freudenthal compactification |G| of G. Now we call G Hamiltonian if there is an infinite cycle in |G| containing all vertices of G. For an introduction see [1]. \nWe examine how to force Hamiltonicity via forbidden induced subgraphs and present recent extensions of results for Hamiltonicity in finite claw-free graphs to locally finite ones. The first two results are about claw- and net-free graphs\, claw- and bull-free graphs\, the last also about further graph classes being structurally richer\, where we focus on paws as relevant subgraphs\, but relax the condition of forbidding them as induced subgraphs. \nThe goal of the talk is twofold: (1) We introduce the history of the topological viewpoint and argue that there are some merits to it (2) sketch the proofs for the results mentioned above in some details. \nThis is based on joint work [4\,5] with Karl Heuer. \nBibliography\n[1] R. Diestel (2017) Infinite Graphs. In: Graph Theory. Graduate Texts in Mathematics\, vol 173. Springer\, Berlin\, Heidelberg. https://doi.org/10.1007/978-3-662-53622-3_8 \n[2] R. Diestel and D. Kühn\, On infinite cycles I\, Combinatorica 24 (2004)\, pp. 69-89. \n[3] R. Diestel and D. Kühn\, On infinite cycles II\, Combinatorica 24 (2004)\, pp. 91-116. \n[4] K. Heuer and D. Sarikaya\, Forcing Hamiltonicity in locally finite graphs via forbidden induced subgraphs I: nets and bulls\, arXiv:2006.09160 \n[5] K. Heuer and D. Sarikaya\, Forcing Hamiltonicity in locally finite graphs via forbidden induced subgraphs II: paws\, arXiv:2006.09166
URL:https://dimag.ibs.re.kr/event/2020-12-03/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
END:VCALENDAR