
Maximum Independent Sets in Subcubic Graphs: New Results
Harutyunyan, Ararat; Lampis, Michael; Lozin, Vadim; Monnot, Jérôme (2019), Maximum Independent Sets in Subcubic Graphs: New Results, in Sau, Ignasi; Thilikos, Dimitrios M., Graph-Theoretic Concepts in Computer Science, Revised Papers, Springer International Publishing : Berlin Heidelberg, p. 40-52. 10.1007/978-3-030-30786-8_4
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Type
Communication / ConférenceDate
2019Conference title
45th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2019)Conference date
2019-06Conference city
Vall de NúriaConference country
SpainBook title
Graph-Theoretic Concepts in Computer Science, Revised PapersBook author
Sau, Ignasi; Thilikos, Dimitrios M.Publisher
Springer International Publishing
Published in
Berlin Heidelberg
ISBN
978-3-030-30785-1
Number of pages
394Pages
40-52
Publication identifier
Metadata
Show full item recordAuthor(s)
Harutyunyan, AraratLaboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Lampis, Michael

Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Lozin, Vadim
Warwick Mathematics Institute [WMI]
Monnot, Jérôme

Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Abstract (EN)
We consider the complexity of the classical Independent Set problem on classes of subcubic graphs characterized by a finite set of forbidden induced subgraphs. It is well-known that a necessary condition for Independent Set to be tractable in such a class (unless P = NP) is that the set of forbidden induced subgraphs includes a subdivided star Sk,k,k, for some k. Here, Sk,k,kis the graph obtained by taking three paths of length k and identifying one of their endpoints.It is an interesting open question whether this condition is also sufficient: is Independent Set tractable on all hereditary classes of subcubic graphs that exclude some Sk,k,k? A positive answer to this question would provide a complete classification of the complexity of Independent Set on all classes of subcubic graphs characterized by a finite set of forbidden induced subgraphs. The best currently known result of this type is tractability for S2,2,2-free graphs. In this paper we generalize this result by showing that the problem remains tractable on S2,k,k-free graphs, for any fixed k. Along the way, we show that subcubic Independent Set is tractable for graphs excluding a type of graph we call an “apple with a long stem”, generalizing known results for apple-free graphs.Subjects / Keywords
Independent set; Sub-Cubic graphs; Apple-Free graphsRelated items
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