Complexity Dichotomy for List-5-Coloring with a Forbidden Induced Subgraph
| dc.contributor.author | Hajebi, Sepehr | |
| dc.contributor.author | Li, Yanjia | |
| dc.contributor.author | Spirkl, Sophie | |
| dc.date.accessioned | 2022-09-01T15:45:21Z | |
| dc.date.available | 2022-09-01T15:45:21Z | |
| dc.date.issued | 2022-08-30 | |
| dc.description | First Published in the Journal of Discrete Mathematics in Volume 36, Issue 3, 2022, published by the Society for Industrial and Applied Mathematics (SIAM). Copyright © by SIAM. Unauthorized reproduction of this article is prohibited. | en |
| dc.description.abstract | For a positive integer r and graphs G and H, we denote by G+H the disjoint union of G and H and by rH the union of r mutually disjoint copies of H. Also, we say G is H-free if H is not isomorphic to an induced subgraph of G. We use Pt to denote the path on t vertices. For a fixed positive integer k, the List-k-Coloring Problem is to decide, given a graph G and a list L(v)⊆{1,…,k} of colors assigned to each vertex v of G, whether G admits a proper coloring ϕ with ϕ(v)∈L(v) for every vertex v of G, and the k-Coloring Problem is the List-k-Coloring Problem restricted to instances with L(v)={1,…,k} for every vertex v of G. We prove that, for every positive integer r, the List-5-Coloring Problem restricted to rP3-free graphs can be solved in polynomial time. Together with known results, this gives a complete dichotomy for the complexity of the List-5-Coloring Problem restricted to H-free graphs: For every graph H, assuming P≠NP, the List-5-Coloring Problem restricted to H-free graphs can be solved in polynomial time if and only if, H is an induced subgraph of either rP3 or P5+rP1 for some positive integer r. As a hardness counterpart, we also show that the k-Coloring Problem restricted to rP4-free graphs is NP-complete for all k≥5 and r≥2. | en |
| dc.description.sponsorship | This research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), funding reference number RGPIN-2020-03912. | en |
| dc.identifier.uri | https://doi.org/10.1137/21M1443352 | |
| dc.identifier.uri | http://hdl.handle.net/10012/18697 | |
| dc.language.iso | en | en |
| dc.publisher | Society for Industrial and Applied Mathematics | en |
| dc.relation.ispartofseries | Journal on Discrete Mathematics; | |
| dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 International | * |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
| dc.subject | coloring | en |
| dc.subject | list coloring | en |
| dc.subject | induced subgraphs | en |
| dc.subject | computational complexity | en |
| dc.title | Complexity Dichotomy for List-5-Coloring with a Forbidden Induced Subgraph | en |
| dc.type | Article | 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 |