{"title":"The complexity of total k-domatic partition and total R-domination on graphs with weak elimination orderings","authors":"Chuan-Min Lee","doi":"10.1080/23799927.2020.1771427","DOIUrl":null,"url":null,"abstract":"In this paper, we propose two linear-time algorithms. One is for computing a weak elimination ordering of a bipartite distance-hereditary graph, and the other one is an alternative algorithm to solve the total R-domination problem for any chordal bipartite graph with a weak elimination ordering. Our two linear-time algorithms lead to a unified approach to several variations of total domination problems for bipartite distance-hereditary graphs. We also show that tthe total 3-domatic partition problem is NP-complete for planar graphs of maximum degree 9 and planar bipartite graphs of maximum degree 12, and show that the 4-domatic partition problem for planar graphs of maximum degree d is polynomial-time reducible to the total 4-domatic partition problem for planar graphs of maximum degree d + 1.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2020-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Computer Mathematics: Computer Systems Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/23799927.2020.1771427","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: 0
Abstract
In this paper, we propose two linear-time algorithms. One is for computing a weak elimination ordering of a bipartite distance-hereditary graph, and the other one is an alternative algorithm to solve the total R-domination problem for any chordal bipartite graph with a weak elimination ordering. Our two linear-time algorithms lead to a unified approach to several variations of total domination problems for bipartite distance-hereditary graphs. We also show that tthe total 3-domatic partition problem is NP-complete for planar graphs of maximum degree 9 and planar bipartite graphs of maximum degree 12, and show that the 4-domatic partition problem for planar graphs of maximum degree d is polynomial-time reducible to the total 4-domatic partition problem for planar graphs of maximum degree d + 1.