Fetching the paper…

Reading the bibliography…

2012

A quasi-tree expansion of the Krushkal polynomial

Butler, Clark

Original
PDF
Post on X

Understand

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 polynomial contains the Bollob\'as-Riordan polynomial of a (possibly nonorientable) ribbon graph as a specialization.
The quasi-tree expansion proven here then extends the recent quasi-tree expansions of the Bollob\'as-Riordan polynomial deduced in the oriented case by A.
Champanerkar et al.

A quasi-tree expansion of the Krushkal polynomial · Around

Built on

W. Tutte, A contribution to the theory of chromatic polynomials
1953
Earlier work this paper cites.
D. J. A. Welsh, Matroid Theory
1976
Earlier work this paper cites.
M. Las Vergnas, On the Tutte polynomial of a morphism of matroids
1980
Earlier work this paper cites.
B. Bollobás and O. Riordan, A polynomial of graphs on surfaces
2002
Earlier work this paper cites.

Similar

A. Champanerkar, I. Kofman, N. Stoltzfus, Graphs on surfaces and Khovanov homology
2007
Cited alongside, same era.
S. Chmutov, Generalized duality for graphs on surfaces and the signed Bollobás-Riordan polynomial
2009
Cited alongside, same era.
I. Moffatt, Partial duality and Bollobás and Riordan’s ribbon graph polynomial
2010
Cited alongside, same era.
R. Askanazi, S. Chmutov, C. Estill, J. Michel, P. Stollenwerk, Polynomial Invariants of Graphs on Surfaces
Original
Cited in the paper.
R. Bradford, C. Butler, S. Chmutov, Arrow Ribbon Graphs
Original
Cited in the paper.
E. Dewey, A quasitree expansion of the Bollobás-Riordan polynomial
Cited in the paper.
J. Ellis-Monaghan, I. Moffatt, Twisted duality and polynomials of embedded graphs
Cited in the paper.
V. Krushkal, D. Renardy, A polynomial invariant and duality for triangulations
Cited in the paper.

Then

A. Champanerkar, I. Kofman, N. Stoltzfus, Quasi-tree expansion for the Bollobás-Riordan-Tutte polynomial
2011
Later among the works it cites.
V. Krushkal, Graphs, Links, and Duality on Surfaces
Original
2011
Later among the works it cites.
F. Vignes-Tourneret, Non-orientable quasi-trees for the Bollobás-Riordan polynomial
2011
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…