Digraphs with All Induced Directed Cycles of the Same Length are not → χ -Bounded
| dc.contributor.author | Carbonero, Alvaro | |
| dc.contributor.author | Hompe, Patrick | |
| dc.contributor.author | Moore, Benjamin | |
| dc.contributor.author | Spirkl, Sophie | |
| dc.date.accessioned | 2022-10-17T16:21:38Z | |
| dc.date.available | 2022-10-17T16:21:38Z | |
| dc.date.issued | 2022-10-07 | |
| dc.description.abstract | For t > 2, let us call a digraph D t-chordal if all induced directed cycles in D have length equal to t. In an earlier paper, we asked for which t it is true that t-chordal graphs with bounded clique number have bounded dichromatic number. Recently, Aboulker, Bousquet, and de Verclos answered this in the negative for t = 3, that is, they gave a construction of 3-chordal digraphs with clique number at most 3 and arbitrarily large dichromatic number. In this paper, we extend their result, giving for each t > 3 a construction of t-chordal digraphs with clique number at most 3 and arbitrarily large dichromatic number, thus answering our question in the negative. On the other hand, we show that a more restricted class, digraphs with no induced directed cycle of length less than t, and no induced directed t-vertex path, have bounded dichromatic number if their clique number is bounded. We also show the following complexity result: for fixed t > 2, the problem of determining whether a digraph is t-chordal is coNP-complete. | en |
| dc.description.sponsorship | This research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), RGPIN-2020-03912. | en |
| dc.identifier.uri | https://doi.org/10.37236/11179 | |
| dc.identifier.uri | http://hdl.handle.net/10012/18888 | |
| dc.language.iso | en | en |
| dc.relation.ispartofseries | Electronic Journal of Combinatorics; | |
| dc.rights | Attribution 4.0 International | * |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | * |
| dc.title | Digraphs with All Induced Directed Cycles of the Same Length are not → χ -Bounded | en |
| dc.type | Article | en |
| dcterms.bibliographicCitation | Carbonero, A., Hompe, P., Moore, B., & Spirkl, S. (2022). Digraphs with All Induced Directed Cycles of the Same Length are not → χ -Bounded. Electronic Journal of Combinatorics, 29(4). https://doi.org/https://doi.org/10.37236/11179 | 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 |
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