28 citations · 75 across the 15 of their papers we have counts for
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math.CO2012★ 4 cited
A quasi-tree expansion of the Krushkal polynomial
Clark Butler
We introduce a generalization of the Krushkal polynomial to nonorientable surfaces, and prove that this polynomial has a natural quasi-tree expansion. This generalized Krushkal pol…
math.CO2011★ 10 cited
Arrow ribbon graphs
Robert Bradford, Clark Butler, Sergei Chmutov
We introduce an additional structure on ribbon graphs, arrow structure. We extend the Bollobás-Riordan polynomial to ribbon graph with this structure. The extended polynomial satis…
math.CO2010
Bollobas-Riordan and relative Tutte polynomials
Clark Butler, Sergei Chmutov
We establish a relation between the Bollobas-Riordan polynomial of a ribbon graph with the relative Tutte polynomial of a plane graph obtained from the ribbon graph using its proje…