The expansion of a chord diagram and the Tutte polynomial

In this paper, it is shown that the chord expansion number f(E) equals the value of the Tutte polynomial at the point (2,−1) for the interlace graph GE corresponding to E. The chord expansion number of a complete multipartite chord diagram is also studied. An extended abstract of the paper was published (Nakamigawa and Sakuma, 2017) [13].