{"title":"A Complete Complexity Dichotomy of the Edge-Coloring Problem for All Sets of \\(8\\)-Edge Forbidden Subgraphs","authors":"D. S. Malyshev, O. I. Duginov","doi":"10.1134/S1990478923040099","DOIUrl":null,"url":null,"abstract":"<p> For a given graph, the edge-coloring problem is to minimize the number of colors sufficient\nto color all the graph edges so that any adjacent edges receive different colors. For all classes\ndefined by sets of forbidden subgraphs, each with 7 edges, the complexity status of this problem is\nknown. In this paper, we obtain a similar result for all sets of 8-edge prohibitions.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"17 4","pages":"791 - 801"},"PeriodicalIF":0.5800,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478923040099","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
For a given graph, the edge-coloring problem is to minimize the number of colors sufficient
to color all the graph edges so that any adjacent edges receive different colors. For all classes
defined by sets of forbidden subgraphs, each with 7 edges, the complexity status of this problem is
known. In this paper, we obtain a similar result for all sets of 8-edge prohibitions.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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