Capturing Logarithmic Space and Polynomial Time on Chordal ClawFree Graphs
Abstract
We show that the class of chordal clawfree graphs admits LREC$_=$definable canonization. LREC$_=$ is a logic that extends firstorder 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 logarithmicspace canonization algorithm, and therefore a logarithmicspace isomorphism test, for the class of chordal clawfree graphs. As a further consequence, LREC$_=$ captures logarithmic space on this graph class. Since LREC$_=$ is contained in fixedpoint logic with counting, we also obtain that fixedpoint logic with counting captures polynomial time on the class of chordal clawfree graphs.
 Publication:

arXiv eprints
 Pub Date:
 February 2018
 arXiv:
 arXiv:1802.10331
 Bibcode:
 2018arXiv180210331G
 Keywords:

 Computer Science  Logic in Computer Science;
 Computer Science  Discrete Mathematics
 EPrint:
 34 pages, 13 figures