Digraph decompositions and Eulerian systems
SIAM Journal on Algebraic and Discrete Methods
Reducing prime graphs and recognizing circle graphs
Combinatorica
A Tutte polynomial for signed graphs
Discrete Applied Mathematics - Combinatorics and complexity
Generalized activites and the Tutte polynomial
Discrete Mathematics
Tutte polynomials computable in polynomial time
Discrete Mathematics - Algebraic graph theory; a volume dedicated to Gert Sabidussi
Journal of Combinatorial Theory Series B
Regular Article: Interval Partitions and Activities for the Greedoid Tutte Polynomial
Advances in Applied Mathematics
The interlace polynomial: a new graph polynomial
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Series and parallel reductions for the Tutte polynomial
Discrete Mathematics
The Combinatorics of Network Reliability
The Combinatorics of Network Reliability
Multimatroids III. Tightness and fundamental graphs
European Journal of Combinatorics - Special issue on combinatorial geometries
The interlace polynomial of graphs at-1
European Journal of Combinatorics
A Two-Variable Interlace Polynomial
Combinatorica
The interlace polynomial of a graph
Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
Distance Hereditary Graphs and the Interlace Polynomial
Combinatorics, Probability and Computing
Journal of Combinatorial Theory Series B
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The interlace polynomials introduced by Arratia, Bollobás and Sorkin extend to invariants of graphs with vertex weights, and these weighted interlace polynomials have several novel properties. One novel property is a version of the fundamental three-term formula $\[ q(G)=q(G-a)+q(G^{ab}-b)+((x-1)^{2}-1)q(G^{ab}-a-b) \]$ that lacks the last term. It follows that interlace polynomial computations can be represented by binary trees rather than mixed binary–ternary trees. Binary computation trees provide a description of q(G) that is analogous to the activities description of the Tutte polynomial. If G is a tree or forest then these ‘algorithmic activities’ are associated with a certain kind of independent set in G. Three other novel properties are weighted pendant-twin reductions, which involve removing certain kinds of vertices from a graph and adjusting the weights of the remaining vertices in such a way that the interlace polynomials are unchanged. These reductions allow for smaller computation trees as they eliminate some branches. If a graph can be completely analysed using pendant-twin reductions, then its interlace polynomial can be calculated in polynomial time. An intuitively pleasing property is that graphs which can be constructed through graph substitutions have vertex-weighted interlace polynomials which can be obtained through algebraic substitutions.