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2010

Polynomial invariants of graphs on surfaces

Askanazi, R., Chmutov, S., Estill, C. et al.

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For a graph embedded into a surface, we relate many combinatorial parameters of the cycle matroid of the graph and the bond matroid of the dual graph with the topological parameters of the embedding.

This will give an expression of the polynomial, defined by M.Las Vergnas in a combinatorial way using matroids as a specialization of the Krushkal polynomial, defined using the symplectic structure in the first homology group of the surface.

Polynomial invariants of graphs on surfaces · Around

Built on

H. Whitney, On the abstract properties of linear dependence
1935
Earlier work this paper cites.
J. Edmonds, On the surface duality of linear graphs
1965
Earlier work this paper cites.
D. J. A. Welsh, Matroid Theory
1976
Earlier work this paper cites.
M. Las Vergnas, Eulerian circuits of 4-valent graphs imbedded in surfaces
1978
Earlier work this paper cites.
M. Las Vergnas, On the Tutte polynomial of a morphism of matroids
1980
Earlier work this paper cites.

Similar

N. White (ed.), Theory of matroids
1986
Cited alongside, same era.
J. Oxley, Matroid theory
1992
Cited alongside, same era.
A. Björner, M. Las Vergnas, B. Sturmfels, N. White, G. Ziegler, Oriented matroids
1993
Cited alongside, same era.
G. Ziegler, Oriented matroids today
1996
Cited alongside, same era.
V. Krushkal, D. Renardy, A polynomial invariant and duality for triangulations
Original
Cited in the paper.

Then

M. Las Vergnas, The Tutte polynomial of a morphism of matroids. I. Set-pointed matroids and matroid perspectives
1999
Later among the works it cites.
S. Yuzvinksy, Orlik-Solomon algebras in algebra and topology
2001
Later among the works it cites.
B. Bollobás and O. Riordan, A polynomial of graphs on surfaces
2002
Later among the works it cites.
V. Krushkal, Graphs, Links, and Duality on Surfaces
2011
Closest in time.

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