Veröffentlichung

Titel:

Saturated simple and 2-simple topological graphs with few edges

AutorInnen:

Péter Hajnal
Alexander Igamberdiev
Günter Rote
André Schulz

Kategorie:

Konferenzbandbeiträge

erschienen in:

International Workshop on Graph-Theoretic Concepts in Computer Science, Springer, Vol. 9224, 2015, pp. 391-405

Abstract:

A simple topological graph is a topological graph in which any two edges have at most one common point, which is either their common endpoint or a proper crossing. More generally, in a k-simple topological graph, every pair of edges has at most k common points of this kind. We construct saturated simple and 2-simple graphs with few edges. These are k-simple graphs in which no further edge can be added. We improve the previous upper bounds of Kynčl, Pach, Radoičić, and Tóth and show that there are saturated simple graphs on n vertices with only 7n edges and saturated 2-simple graphs on n vertices with 14.5n edges. As a consequence, 14.5n edges is also a new upper bound for k-simple graphs (considering all values of k). We also construct saturated simple and 2-simple graphs that have some vertices with low degree.

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arXiv

BibTeX-Eintrag:

@inproceedings{hirs-ss2st-16 , author = {P\'eter Hajnal and Alexander Igamberdiev and G{\"u}nter Rote and Andr\'e Schulz} , title = {Saturated simple and 2-simple topological graphs with few edges} , year = {2016} , month = jun , volume = {9224} , pages = {391--405} , booktitle = {41st International Workshop on Graph-Theoretic Concepts in Computer Science---WG 2015} , editor = {Ernst Mayr} , publisher = {Springer-Verlag} , series = {Lecture Notes in Computer Science} , url = {http://page.mi.fu-berlin.de/rote/Papers/pdf/Saturated+simple+and+2-simple+topological+graphs+with+few+edges.pdf} , eprint = {arXiv:1503.01386} , doi = {10.1007/978-3-662-53174-7_28} }