On Weak Flexibility in Planar Graphs
dc.contributor.author | Lidicky, Bernard | |
dc.contributor.author | Lidicky, Bernard | |
dc.contributor.author | Masarík, Tomáš | |
dc.contributor.author | Murphy, Kyle | |
dc.contributor.author | Zerbib, Shira | |
dc.contributor.department | Mathematics | |
dc.date | 2020-09-22T17:58:21.000 | |
dc.date.accessioned | 2021-02-26T02:54:43Z | |
dc.date.available | 2021-02-26T02:54:43Z | |
dc.date.copyright | Wed Jan 01 00:00:00 UTC 2020 | |
dc.date.issued | 2020-09-16 | |
dc.description.abstract | <p>Recently, Dvořák, Norin, and Postle introduced flexibility as an extension of list coloring on graphs [JGT 19']. In this new setting, each vertex v in some subset of V(G) has a request for a certain color r(v) in its list of colors L(v). The goal is to find an L coloring satisfying many, but not necessarily all, of the requests.</p> <p>The main studied question is whether there exists a universal constant ϵ>0 such that any graph G in some graph class C satisfies at least ϵ proportion of the requests. More formally, for k>0 the goal is to prove that for any graph G∈C on vertex set V, with any list assignment L of size k for each vertex, and for every R⊆V and a request vector (r(v):v∈R, r(v)∈L(v)), there exists an L-coloring of G satisfying at least ϵ|R| requests. If this is true, then C is called ϵ-flexible for lists of size k.</p> <p>Choi et al. [arXiv 20'] introduced the notion of weak flexibility, where R=V. We further develop this direction by introducing a tool to handle weak flexibility. We demonstrate this new tool by showing that for every positive integer b there exists ϵ(b)>0 so that the class of planar graphs without K4,C5,C6,C7,Bb is weakly ϵ(b)-flexible for lists of size 4 (here Kn, Cn and Bn are the complete graph, a cycle, and a book on n vertices, respectively). We also show that the class of planar graphs without K4,C5,C6,C7,B5 is ϵ-flexible for lists of size 4. The results are tight as these graph classes are not even 3-colorable.</p> | |
dc.description.comments | <p>This preprint is made available though arXiv: <a href="https://arxiv.org/abs/2009.07932" target="_blank">https://arxiv.org/abs/2009.07932</a>. </p> | |
dc.format.mimetype | application/pdf | |
dc.identifier | archive/lib.dr.iastate.edu/math_pubs/258/ | |
dc.identifier.articleid | 1265 | |
dc.identifier.contextkey | 19510268 | |
dc.identifier.s3bucket | isulib-bepress-aws-west | |
dc.identifier.submissionpath | math_pubs/258 | |
dc.identifier.uri | https://dr.lib.iastate.edu/handle/20.500.12876/96653 | |
dc.language.iso | en | |
dc.source.bitstream | archive/lib.dr.iastate.edu/math_pubs/258/2020_Lidicky_WeakFlexibilityPreprint.pdf|||Fri Jan 14 22:59:41 UTC 2022 | |
dc.subject.disciplines | Discrete Mathematics and Combinatorics | |
dc.subject.disciplines | Mathematics | |
dc.title | On Weak Flexibility in Planar Graphs | |
dc.type | article | |
dc.type.genre | article | |
dspace.entity.type | Publication | |
relation.isAuthorOfPublication | a1d8f5ab-9124-4104-981c-8ba1e426e3ff | |
relation.isOrgUnitOfPublication | 82295b2b-0f85-4929-9659-075c93e82c48 |
File
Original bundle
1 - 1 of 1
No Thumbnail Available
- Name:
- 2020_Lidicky_WeakFlexibilityPreprint.pdf
- Size:
- 847.27 KB
- Format:
- Adobe Portable Document Format
- Description: