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Capturing Logarithmic Space and Polynomial Time on Chordal Claw-Free Graphs Grußien, Berit Descriptive complexity logarithmic space polynomial time chordal claw-free graphs 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Berit Grußien 2017 Is Part Of LIPIcs, Volume 82, 26th EACSL Annual Conference on Computer Science Logic (CSL 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CSL.2017.26 urn:nbn:de:0030-drops-76900 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2017.26 eng https://creativecommons.org/licenses/by/3.0/legalcode