Sparsification Lower Bounds for List H -Coloring

IF 0.8 Q3 COMPUTER SCIENCE, THEORY & METHODS ACM Transactions on Computation Theory Pub Date : 2023-09-15 DOI:10.1145/3612938
Hubie Chen, Bart M. P. Jansen, Karolina Okrasa, Astrid Pieterse, Paweł Rzążewski
{"title":"Sparsification Lower Bounds for List <i>H</i> -Coloring","authors":"Hubie Chen, Bart M. P. Jansen, Karolina Okrasa, Astrid Pieterse, Paweł Rzążewski","doi":"10.1145/3612938","DOIUrl":null,"url":null,"abstract":"We investigate the List H -Coloring problem, the generalization of graph coloring that asks whether an input graph G admits a homomorphism to the undirected graph H (possibly with loops), such that each vertex v ∈ V ( G ) is mapped to a vertex on its list L ( v )⊆ V ( H ). An important result by Feder, Hell, and Huang [JGT 2003] states that List H -Coloring is polynomial-time solvable if H is a so-called bi-arc graph , and NP-complete otherwise. We investigate the NP-complete cases of the problem from the perspective of polynomial-time sparsification: can an n -vertex instance be efficiently reduced to an equivalent instance of bitsize \\(\\mathcal {O}(n^{2-\\varepsilon }) \\) for some ε &gt; 0? We prove that if H is not a bi-arc graph, then List H -Coloring does not admit such a sparsification algorithm unless \\({\\mathsf {NP \\subseteq coNP/poly}} \\) . Our proofs combine techniques from kernelization lower bounds with a study of the structure of graphs H which are not bi- graphs.","PeriodicalId":44045,"journal":{"name":"ACM Transactions on Computation Theory","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM Transactions on Computation Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3612938","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 1

Abstract

We investigate the List H -Coloring problem, the generalization of graph coloring that asks whether an input graph G admits a homomorphism to the undirected graph H (possibly with loops), such that each vertex v ∈ V ( G ) is mapped to a vertex on its list L ( v )⊆ V ( H ). An important result by Feder, Hell, and Huang [JGT 2003] states that List H -Coloring is polynomial-time solvable if H is a so-called bi-arc graph , and NP-complete otherwise. We investigate the NP-complete cases of the problem from the perspective of polynomial-time sparsification: can an n -vertex instance be efficiently reduced to an equivalent instance of bitsize \(\mathcal {O}(n^{2-\varepsilon }) \) for some ε > 0? We prove that if H is not a bi-arc graph, then List H -Coloring does not admit such a sparsification algorithm unless \({\mathsf {NP \subseteq coNP/poly}} \) . Our proofs combine techniques from kernelization lower bounds with a study of the structure of graphs H which are not bi- graphs.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
列表H -着色的稀疏化下界
我们研究了列表H -着色问题,这是图着色的推广,它询问输入图G是否与无向图H(可能有环)同态,使得每个顶点v∈v (G)映射到其列表L (v)上的一个顶点v (H)。Feder, Hell和Huang [JGT 2003]的一个重要结果表明,如果H是所谓的双弧图,则列表H -着色是多项式时间可解的,否则是np完全的。我们从多项式时间稀疏化的角度研究了该问题的np完全情况:对于某些ε &gt, n顶点实例是否可以有效地简化为位大小为\(\mathcal {O}(n^{2-\varepsilon }) \)的等效实例;0?我们证明了如果H不是双弧图,那么List H -Coloring不允许这样的稀疏化算法,除非\({\mathsf {NP \subseteq coNP/poly}} \)。我们的证明结合了核化下界的技术和对非双图的图H结构的研究。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
ACM Transactions on Computation Theory
ACM Transactions on Computation Theory COMPUTER SCIENCE, THEORY & METHODS-
CiteScore
2.30
自引率
0.00%
发文量
10
期刊最新文献
Small-Space Spectral Sparsification via Bounded-Independence Sampling Tight Sum-of-Squares lower bounds for binary polynomial optimization problems Optimal Polynomial-time Compression for Boolean Max CSP On p -Group Isomorphism: search-to-decision, counting-to-decision, and nilpotency class reductions via tensors Quantum communication complexity of linear regression
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1