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, and therefore a logarithmic-space isomorphism test, for the class of chordal claw-free graphs. As a further consequence, 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.
翻译:我们显示,无铬爪子图形的等级允许LREC=可定义的罐头化。 LREC=是一个逻辑逻辑,它扩展了第一阶逻辑,由操作员进行计算,使其能够正式确定有限的循环形式。这个操作员可以在对数空间中进行评估。由此可见,对数空间罐化算法存在一种对数-空间孔化算法,因此也存在对数-空间无爪子图形的对数形态化测试。另一个结果是,LREC=在这个图形类别中捕获对数空间。由于LREC=包含在固定点逻辑中进行计算,我们还获得了固定点逻辑,在相形弧爪子无爪子图形的等级上计算捕捉多点时间。