In this paper we present a new termination proof and complexity analysis of unfolding graph rewriting which is a specific kind of infinite graph rewriting expressing the general form of safe recursion. We introduce a termination order over sequences of terms together with an interpretation of term graphs into sequences of terms. Unfolding graph rewrite rules expressing general safe recursion ca...

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Gene rearrangements within the process of gene assembly in ciliates can be represented using a 4-regular graph. Based on this observation, Burns et al. [Discrete Appl. Math., 2013] propose a graph polynomial abstracting basic features of the assembly process, like the number of segments excised. We show that this assembly polynomial is essentially (i) a single variable case of the transition po...

A potential maximal clique of a graph is a vertex set that induces a maximal clique in some minimal triangulation of that graph. It is known that if these objects can be listed in polynomial time for a class of graphs, the treewidth and the minimum 5ll-in are polynomially tractable for these graphs. We show here that the potential maximal cliques of a graph can be generated in polynomial time i...

The celebrated Thistlethwaite theorem relates the Jones polynomial of a link with the Tutte polynomial of the corresponding planar graph. We give a generalization of this theorem to virtual links. In this case, the graph will be embedded into a (higher genus) surface. For such graphs we use the generalization of the Tutte polynomial discovered by B. Bollobás and O. Riordan.

We show that for any k there is a polynomial time algorithm to evaluate the weighted graph polynomial U of any graph with tree-width at most k at any point. For a graph with n vertices, the algorithm requires O(akn 2k+3) arithmetical operations, where ak depends only on k.