  There are two oriented 4-valent graphical models for the Kauffman polynomial:
one (HJ) is obtained by combining Jaeger's formula and Kauffman-Vogel model for
the Homflypt polynomial; the other (WF) is obtained by combining Kauffman-Vogel
model for the Kauffman polynomial and Wu's formula. The main goal of this paper
is to explore the relationship between the two models. We find that there is an
one-to-many correspondence between the terms of HJ model and the terms of WF
model. In addition, we investigate the relation between trivalent graphical
models and 4-valent graphical models of both the Homflypt and Kauffman
polynomials, and observe that there is a bijection between the terms of the two
models.
