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dc.contributor.authorHompe, Patrick
dc.contributor.authorPelikánová, Petra
dc.contributor.authorPokorná, Aneta
dc.contributor.authorSpirkl, Sophie
dc.date.accessioned2022-08-11 23:27:13 (GMT)
dc.date.available2022-08-11 23:27:13 (GMT)
dc.date.issued2021-05-01
dc.identifier.urihttps://doi.org/10.1016/j.disc.2021.112319
dc.identifier.urihttp://hdl.handle.net/10012/18506
dc.descriptionThe final publication is available at Elsevier via https://doi.org/10.1016/j.disc.2021.112319. © 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/en
dc.description.abstractFor a digraph G and v is an element of V(G), let delta(+)(v) be the number of out-neighbors of v in G. The Caccetta-Haggkvist conjecture states that for all k >= 1, if G is a digraph with n = |V(G)| such that delta(+)(v) >= k for all v is an element of V(G), then G contains a directed cycle of length at most [n/k]. In Aharoni et al. (2019), Aharoni proposes a generalization of this conjecture, that a simple edge-colored graph on n vertices with n color classes, each of size k, has a rainbow cycle of length at most.n/k.. In this paper, we prove this conjecture if each color class has size Omega(k log k).en
dc.description.sponsorshipThis paper is partially based on research performed at the DIMACS REU 2019, which has been supported by the H2020-MSCA-RISE project CoSP- GA No. 823748. Supported by GAUK 1277018. This material is based upon work supported by the National Science Foundation under Award No. DMS-1802201. We acknowledge the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), [funding reference number RGPIN-2020-03912]. Cette recherche a ´et´e financ´ee par le Conseil de recherches en sciences naturelles et en g´enie du Canada (CRSNG), [num´ero de r´ef´erence RGPIN-2020-03912].en
dc.language.isoenen
dc.publisherElsevieren
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subjectdirected graphen
dc.subjectrainbowen
dc.subjectCaccetta–Haggkvist conjectureen
dc.subjectdirected cycleen
dc.titleOn Aharoni’s rainbow generalization of the Caccetta–Häggkvist conjectureen
dc.typeArticleen
dcterms.bibliographicCitationHompe, P., Pelikánová, P., Pokorná, A., & Spirkl, S. (2021). On Aharoni’s rainbow generalization of the Caccetta–Häggkvist conjecture. Discrete Mathematics, 344(5), 112319. https://doi.org/10.1016/j.disc.2021.112319en
uws.contributor.affiliation1Faculty of Mathematicsen
uws.contributor.affiliation2Combinatorics and Optimizationen
uws.typeOfResourceTexten
uws.peerReviewStatusRevieweden
uws.scholarLevelFacultyen


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