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Decomposing almost complete graphs by random trees
dc.contributor.author | Lladó Sánchez, Ana M. |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2018-05-15T08:30:59Z |
dc.date.available | 2020-02-01T01:25:37Z |
dc.date.issued | 2018-02 |
dc.identifier.citation | Llado, A. Decomposing almost complete graphs by random trees. "Journal of combinatorial theory. Series A", Febrer 2018, vol. 154, p. 406-421. |
dc.identifier.issn | 0097-3165 |
dc.identifier.uri | http://hdl.handle.net/2117/117218 |
dc.description.abstract | An old conjecture of Ringel states that every tree with m edges decomposes the complete graph K2m+1. The best known lower bound for the order of a complete graph which admits a decomposition by every given tree with m edges is O(m3). We show that asymptotically almost surely a random tree with m edges and p=2m+1 a prime decomposes K2m+1(r) for every r=2, the graph obtained from the complete graph K2m+1 by replacing each vertex by a coclique of order r. Based on this result we show, among other results, that a random tree with m+1 edges a.a.s. decomposes the compete graph K6m+5 minus one edge. |
dc.format.extent | 16 p. |
dc.language.iso | eng |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs |
dc.subject.lcsh | Graph theory |
dc.subject.other | Graph decomposition |
dc.subject.other | Polynomial method |
dc.subject.other | Ringel's conjecture |
dc.title | Decomposing almost complete graphs by random trees |
dc.type | Article |
dc.subject.lemac | Grafs, Teoria de |
dc.contributor.group | Universitat Politècnica de Catalunya. GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics |
dc.identifier.doi | 10.1016/j.jcta.2017.09.008 |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::05 Combinatorics::05C Graph theory |
dc.relation.publisherversion | http://www.sciencedirect.com/science/article/pii/S0097316517301322?via%3Dihub |
dc.rights.access | Open Access |
local.identifier.drac | 21623586 |
dc.description.version | Postprint (author's final draft) |
local.citation.author | Llado, A. |
local.citation.publicationName | Journal of combinatorial theory. Series A |
local.citation.volume | 154 |
local.citation.startingPage | 406 |
local.citation.endingPage | 421 |
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