Split Permutation Graphs

The class of split permutation graphs is the intersection of two important classes, the split graphs and permutation graphs. It also contains an important subclass, the threshold graphs. The class of threshold graphs enjoys many nice properties. In particular, these graphs have bounded clique-width...

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Bibliographic Details
Published inGraphs and combinatorics Vol. 30; no. 3; pp. 633 - 646
Main Authors Korpelainen, Nicholas, Lozin, Vadim V., Mayhill, Colin
Format Journal Article
LanguageEnglish
Published Tokyo Springer Japan 01.05.2014
Springer Nature B.V
Subjects
Combinatorial analysis
Combinatorics
Engineering Design
Extensibility
Graphs
Intersections
Mathematics
Mathematics and Statistics
Original Paper
Permutations
Thresholds
Split graphs
Well-quasi-order
Permutation graphs
Clique-width
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Summary:The class of split permutation graphs is the intersection of two important classes, the split graphs and permutation graphs. It also contains an important subclass, the threshold graphs. The class of threshold graphs enjoys many nice properties. In particular, these graphs have bounded clique-width and they are well-quasi-ordered by the induced subgraph relation. It is known that neither of these two properties is extendable to split graphs or to permutation graphs. In the present paper, we study the question of extendability of these two properties to split permutation graphs. We answer this question negatively with respect to both properties. Moreover, we conjecture that with respect to both of them the split permutation graphs constitute a critical class.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-013-1290-3