DC Field | Value | Language |
---|---|---|
dc.contributor.author | Holmsen, Andreas | ko |
dc.contributor.author | Kim, Minki | ko |
dc.contributor.author | Lee, Seunghun | ko |
dc.date.accessioned | 2019-06-24T01:30:07Z | - |
dc.date.available | 2019-06-24T01:30:07Z | - |
dc.date.created | 2019-06-04 | - |
dc.date.issued | 2019-06 | - |
dc.identifier.citation | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v.371, no.12, pp.8755 - 8779 | - |
dc.identifier.issn | 0002-9947 | - |
dc.identifier.uri | http://hdl.handle.net/10203/262789 | - |
dc.description.abstract | We make the first step towards a "nerve theorem" for graphs. Let G be a simple graph and let F be a family of induced subgraphs of G such that the intersection of any members of F is either empty or connected. We show that if the nerve complex of F has non-vanishing homology in dimension three, then G contains the complete graph on five vertices as a minor. As a consequence we confirm a conjecture of Goaoc concerning an extension of the planar (p, q) theorem due to Alon and Kleitman: Let F be a finite family of open connected sets in the plane such that the intersection of any members of F is either empty or connected. If among any p >= 3 members of F there are some three that intersect, then there is a set of C points which intersects every member of F, where C is a constant depending only on p. | - |
dc.language | English | - |
dc.publisher | AMER MATHEMATICAL SOC | - |
dc.title | NERVES, MINORS, AND PIERCING NUMBERS | - |
dc.type | Article | - |
dc.identifier.wosid | 000469495300017 | - |
dc.type.rims | ART | - |
dc.citation.volume | 371 | - |
dc.citation.issue | 12 | - |
dc.citation.beginningpage | 8755 | - |
dc.citation.endingpage | 8779 | - |
dc.citation.publicationname | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | - |
dc.identifier.doi | 10.1090/tran/7608 | - |
dc.contributor.localauthor | Holmsen, Andreas | - |
dc.description.isOpenAccess | N | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordPlus | CONVEX-SETS | - |
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