We provide a unified framework in which the interlace polynomial and severalrelated graph polynomials are defined more generally for multimatroids anddelta-matroids. Using combinatorial properties of multimatroids rather thangraph-theoretical arguments, we find that various known results about thesepolynomials, including their recursive relations, are both more efficiently andmore generally obtained. In addition, we obtain several interrelationships andresults for polynomials on multimatroids and delta-matroids that correspond tonew interrelationships and results for the corresponding graphs polynomials. Asa tool we prove the equivalence of tight 3-matroids and delta-matroids closedunder the operations of twist and loop complementation, called vf-safedelta-matroids. This result is of independent interest and related to theequivalence between tight 2-matroids and even delta-matroids observed byBouchet.
展开▼
