Abstract

The notion of augmenting graphs generalizes Berge's idea of augmenting chains, which was used by Edmonds in his celebrated solution of the maximum matching problem. This problem is a special case of the more general maximum independent set (MIS) problem. Recently, the augmenting graph approach has been successfully applied to solve MIS in various other special cases. However, our knowledge of augmenting graphs is still very limited and we do not even know what the minimal infinite classes of augmenting graphs are. In the present paper, we find an answer to this question and apply it to extend the area of polynomial-time solvability of the maximum independent set problem.

Highlights

  • IntroductionAn independent set is a subset of pairwise non-adjacent vertices. For an input graph G, the maximum independent set (MIS) problem asks to find the maximum cardinality (denoted α(G)) of an independent set in G

  • In a graph, an independent set is a subset of pairwise non-adjacent vertices

  • In the last 15 years, the augmenting graph approach was frequently applied to various graph classes to design polynomial-time algorithms for the maximum independent set problem and many new types of augmenting graphs have been discovered in the literature

Read more

Summary

Introduction

An independent set is a subset of pairwise non-adjacent vertices. For an input graph G, the maximum independent set (MIS) problem asks to find the maximum cardinality (denoted α(G)) of an independent set in G. Since it has been understood that the idea of augmenting chains is just a (very) special case of a general approach to solve the maximum independent set problem, known as the augmenting graph technique. In the last 15 years, the augmenting graph approach was frequently applied to various graph classes to design polynomial-time algorithms for the maximum independent set problem and many new types of augmenting graphs have been discovered in the literature (see [6] for a survey). Our result allows us to identify new classes of graphs with polynomial-time solvable maximum independent set problem that extend some of the previously known results, such as algorithms for claw-free graphs and (Pk, K1,t )-free graphs. We denote such a graph by (W, B, E), where W and B are the respective independent sets and E is the set of edges

Augmenting Graphs
Minimal Infinite Classes of Augmenting Graphs
Conclusion
Full Text
Paper version not known

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.