Complexity of Ck-Coloring in Hereditary Classes of Graphs
| dc.contributor.author | Chudnovsky, Maria | |
| dc.contributor.author | Huang, Shenwei | |
| dc.contributor.author | Rzążewski, Paweł | |
| dc.contributor.author | Spirkl, Sophie | |
| dc.contributor.author | Zhong, Mingxian | |
| dc.date.accessioned | 2022-08-12T01:13:36Z | |
| dc.date.available | 2022-08-12T01:13:36Z | |
| dc.date.issued | 2019 | |
| dc.description.abstract | For a graph F, a graph G is F-free if it does not contain an induced subgraph isomorphic to F. For two graphs G and H, an H-coloring of G is a mapping f : V (G) --> V (H) such that for every edge uv E(G) it holds that f(u)f(v) E(H). We are interested in the complexity of the problem H-Coloring, which asks for the existence of an H-coloring of an input graph G. In particular, we consider H-Coloring of F-free graphs, where F is a fixed graph and H is an odd cycle of length at least 5. This problem is closely related to the well known open problem of determining the complexity of 3-Coloring of Pt-free graphs. We show that for every odd k ≥ 5 the Ck-Coloring problem, even in the precoloring-extension variant, can be solved in polynomial time in P9-free graphs. On the other hand, we prove that the extension version of Ck-Coloring is NP-complete for F-free graphs whenever some component of F is not a subgraph of a subdivided claw. | en |
| dc.description.sponsorship | Supported by NSF grant DMS-1763817. This material is based upon work supported in part by the U. S. Army Research Laboratory and the U. S. Army Research Office under grant number W911NF-16-1-0404. This research is supported by the National Natural Science Foundation of China (11801284). This material is based upon work supported by the National Science Foundation under Award No. DMS1802201. | en |
| dc.identifier.uri | https://doi.org/10.4230/LIPIcs.ESA.2019.31 | |
| dc.identifier.uri | http://hdl.handle.net/10012/18531 | |
| dc.language.iso | en | en |
| dc.publisher | Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik | en |
| dc.rights | Attribution 4.0 International | * |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | * |
| dc.subject | homomorphism | en |
| dc.subject | hereditary class | en |
| dc.subject | computational complexity | en |
| dc.subject | forbidden induced subgraph | en |
| dc.title | Complexity of Ck-Coloring in Hereditary Classes of Graphs | en |
| dc.type | Conference Paper | en |
| dcterms.bibliographicCitation | Chudnovsky, M., Huang, S., Rzazewski, P., Spirkl, S., & Zhong, M. (2019). Complexity of C_k-Coloring in Hereditary Classes of Graphs. In M. A. Bender, O. Svensson, & G. Herman (Eds.), 27th Annual European Symposium on Algorithms (ESA 2019) (Vol. 144, p. 31:1-31:15). Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik. https://doi.org/10.4230/LIPIcs.ESA.2019.31 | 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 |