On Aharoni’s rainbow generalization of the Caccetta–Häggkvist conjecture
| dc.contributor.author | Hompe, Patrick | |
| dc.contributor.author | Pelikánová, Petra | |
| dc.contributor.author | Pokorná, Aneta | |
| dc.contributor.author | Spirkl, Sophie | |
| dc.date.accessioned | 2022-08-11T23:27:13Z | |
| dc.date.available | 2022-08-11T23:27:13Z | |
| dc.date.issued | 2021-05-01 | |
| dc.description | The 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.abstract | For 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.sponsorship | This 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.identifier.uri | https://doi.org/10.1016/j.disc.2021.112319 | |
| dc.identifier.uri | http://hdl.handle.net/10012/18506 | |
| dc.language.iso | en | en |
| dc.publisher | Elsevier | en |
| dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 International | * |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
| dc.subject | directed graph | en |
| dc.subject | rainbow | en |
| dc.subject | Caccetta–Haggkvist conjecture | en |
| dc.subject | directed cycle | en |
| dc.title | On Aharoni’s rainbow generalization of the Caccetta–Häggkvist conjecture | en |
| dc.type | Article | en |
| dcterms.bibliographicCitation | Hompe, 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.2021.112319 | en |
| uws.contributor.affiliation1 | Faculty of Mathematics | en |
| uws.contributor.affiliation2 | Combinatorics and Optimization | en |
| uws.peerReviewStatus | Reviewed | en |
| uws.scholarLevel | Faculty | en |
| uws.typeOfResource | Text | en |