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.
@InProceedings{gruien:LIPIcs.CSL.2017.26, author = {Gru{\ss}ien, Berit}, 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 = {Goranko, Valentin and Dam, Mads}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2017.26}, URN = {urn:nbn:de:0030-drops-76900}, doi = {10.4230/LIPIcs.CSL.2017.26}, annote = {Keywords: Descriptive complexity, logarithmic space, polynomial time, chordal claw-free graphs} }
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