Graph polynomials serve as robust algebraic encodings of the intricate combinatorial properties inherent to graphs. At the heart of this discipline lies the Tutte polynomial, an invariant that not ...

A realizable degree sequence can be realized in many ways as a graph. There are several tests for determining realizability of a degree sequence. Up to now, not much was known about the common ...

We prove necessary and sufficient conditions for an arbitrary invariant of braids with m double points to be the ``mth derivative'' of a braid invariant. We show that the "primary obstruction to ...