Critical elements in combinatorially closed families of graph classes

The notions of boundary and minimal hard classes of graphs, united by the term “critical classes,” are useful tools for analysis of computational complexity of graph problems in the family of hereditary graph classes. In this family, boundary classes are known for several graph problems. In the pape...

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Bibliographic Details
Published in:Journal of applied and industrial mathematics Vol. 11; no. 1; pp. 99 - 106
Main Author: Malyshev, D. S.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.01.2017
Springer Nature B.V
Subjects:
Algorithms
Approximation
Bandwidth
Bandwidths
Boundaries
Boundary conditions
Computer programs
Descriptions
Graph theory
Graphs
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Studies
hereditary class
critical class
efficient algorithm
computational complexity
ISSN:1990-4789, 1990-4797
Online Access:Get full text
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Summary:The notions of boundary and minimal hard classes of graphs, united by the term “critical classes,” are useful tools for analysis of computational complexity of graph problems in the family of hereditary graph classes. In this family, boundary classes are known for several graph problems. In the paper, we consider critical graph classes in the families of strongly hereditary and minor closed graph classes. Prior to our study, there was the only one example of a graph problem for which boundary classes were completely described in the family of strongly hereditary classes. Moreover, no boundary classes were known for any graph problem in the family of minor closed classes. In this article, we present several complete descriptions of boundary classes for these two families and some classical graph problems. For the problem of 2-additive approximation of graph bandwidth, we find a boundary class in the family of minor closed classes. Critical classes are not known for this problem in the other two families of graph classes.
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ISSN:1990-4789
1990-4797
DOI:10.1134/S1990478917010112