On the arc index of Kanenobu knots.

In this paper, we calculate the Kauffman polynomials of Kanenobu knots with half twists and determine their spans on the variable completely. As an application, we determine the arc index of infinitely many Kanenobu knots. In particular, we give sharper lower bounds of the arc index of by using canonical cabling algorithm and the 2-cable -polynomials. Moreover, we give sharper upper bounds of the arc index of some Kanenobu knots by using their braid presentations. [ABSTRACT FROM AUTHOR]