When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2017.26
URN: urn:nbn:de:0030-drops-76900
URL: http://drops.dagstuhl.de/opus/volltexte/2017/7690/
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Capturing Logarithmic Space and Polynomial Time on Chordal Claw-Free Graphs

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Abstract

We show that the class of chordal claw-free graphs admits LREC=-definable canonization. LREC= is a logic that extends first-order logic with counting by an operator that allows it to formalize a limited form of recursion. This operator can be evaluated in logarithmic space. It follows that there exists a logarithmic-space canonization algorithm for the class of chordal claw-free graphs, and that LREC= captures logarithmic space on this graph class. Since LREC= is contained in fixed-point logic with counting, we also obtain that fixed-point logic with counting captures polynomial time on the class of chordal claw-free graphs.

BibTeX - Entry

```@InProceedings{gruien:LIPIcs:2017:7690,
author =	{Berit Gru{\ss}ien},
title =	{{Capturing Logarithmic Space and Polynomial Time on Chordal Claw-Free Graphs}},
booktitle =	{26th EACSL Annual Conference on Computer Science Logic (CSL 2017)},
pages =	{26:1--26:19},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-95977-045-3},
ISSN =	{1868-8969},
year =	{2017},
volume =	{82},
editor =	{Valentin Goranko and Mads Dam},
publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},