Local coloring: New observations and new reductions

Jie You, Yixin Cao, Jianxin Wang

Research output: Chapter in book / Conference proceedingConference article published in proceeding or bookAcademic researchpeer-review

Abstract

A k-coloring of a graph is an assignment of integers between 1 and k to vertices in the graph such that the endpoints of each edge receive different numbers. We study a local variation of the coloring problem, which imposes further requirements on every set of three vertices: We are not allowed to use two consecutive numbers for a path on three vertices, or three consecutive numbers for a cycle on three vertices. Given a graph G and a positive integer k, the local coloring problem asks for whether G admits a local k-coloring. We show that it cannot be solved in subexponential time, unless the Exponential Time Hypothesis fails, and a new reduction for the NP-hardness of this problem. Our structural observations behind these reductions are of independent interests. We close the paper with a short remark on local colorings of perfect graphs.

Original languageEnglish
Title of host publicationFrontiers in Algorithmics - 13th International Workshop, FAW 2019, Proceedings
EditorsMei Lu, Yijia Chen, Xiaotie Deng
PublisherSpringer-Verlag
Pages51-62
Number of pages12
ISBN (Print)9783030181253
DOIs
Publication statusPublished - 1 Jan 2019
Event13th International Workshop on Frontiers in Algorithmics, FAW 2019 - Sanya, China
Duration: 29 Apr 20193 May 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11458 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference13th International Workshop on Frontiers in Algorithmics, FAW 2019
Country/TerritoryChina
CitySanya
Period29/04/193/05/19

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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