Bipartite partial duals and circuits in medial graphs
arXiv:1106.4189 · doi:10.1007/s00493-013-2850-0
Abstract
It is well known that a plane graph is Eulerian if and only if its geometric dual is bipartite. We extend this result to partial duals of plane graphs. We then characterize all bipartite partial duals of a plane graph in terms of oriented circuits in its medial graph.
v2: minor changes. To appear in Combinatorica
References in corpus (9)
- The multivariate signed Bollobas-Riordan polynomial
- Twisted duality for embedded graphs
- Topological graph polynomials and quantum field theory, Part II: Mehler kernel theories
- Partial duality and Bollobas and Riordan's ribbon graph polynomial
- Unsigned state models for the Jones polynomial
- A characterization of partially dual graphs
- Non-orientable quasi-trees for the Bollobas-Riordan polynomial
- Partial duals of plane graphs, separability and the graphs of knots
- On the Seifert graphs of a link diagram and its parallels
Cited by in corpus (9)
- On the interplay between embedded graphs and delta-matroids
- Separability and the genus of a partial dual
- Matroids, Delta-matroids and Embedded Graphs
- On a conjecture of Gross, Mansour and Tucker
- New Dualities From Old: generating geometric, Petrie, and Wilson dualities and trialites of ribbon graphs
- Checkerboard colourable twisted duals
- Characterizations of Eulerian and even-face partial duals of ribbon graphs
- On the degree sequences of dual graphs on surfaces
- Eulerian and bipartite binary delta-matroids