Bipartite minors

@article{Chudnovsky2016BipartiteM,
  title={Bipartite minors},
  author={M. Chudnovsky and G. Kalai and Eran Nevo and I. Novik and P. Seymour},
  journal={J. Comb. Theory, Ser. B},
  year={2016},
  volume={116},
  pages={219-228}
}
We introduce a notion of bipartite minors and prove a bipartite analog of Wagner's theorem: a bipartite graph is planar if and only if it does not contain K 3 , 3 as a bipartite minor. Similarly, we provide a forbidden minor characterization for outerplanar graphs and forests. We then establish a recursive characterization of bipartite ( 2 , 2 ) -Laman graphs - a certain family of graphs that contains all maximal bipartite planar graphs. 
Bipartite and Eulerian minors
  • D. Wagner
  • Mathematics, Computer Science
  • Eur. J. Comb.
  • 2018
TLDR
This result on Eulerian minors in binary matroids extends a result of Chudnovsky et al. who characterized planar graphs within the class of bipartite graphs by the exclusion of K 3, 3 as a bipartites minor. Expand
A note on immersion minors and planarity
  • D. Wagner
  • Mathematics, Computer Science
  • Discret. Math.
  • 2018
TLDR
By placing a simple restriction on the immersion-minor operations, all immersion minors of a planar graph are planar, which allows one to easily obtain a characterization of planar graphs using immersion minors. Expand
Excluded checkerboard colourable ribbon graph minors.
In this paper, we first introduce the notions of checkerboard colourable minors for ribbon graphs motivated by the Eulerian ribbon graph minors, and two kinds of bipartite minors for ribbon graphs,Expand
Extremal embedded graphs
TLDR
The notion of extremal minor is introduced and provided an excluded extremalMinor characterization for extremal ribbon graphs and two related conjectures raised by Huggett and Tawfik hold for more general ribbon graphs. Expand
Eulerian and even-face ribbon graph minors
TLDR
These minors preserve Eulerian and even-face properties of ribbon graphs, respectively, and are then characterized using these minors. Expand

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Über eine Eigenschaft der ebenen Komplexe
*) Z ∪ Y s is critical
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10*) Z ∪ Y s is critical
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Bipartite rigidity. Trans. Amer. Math. Soc
  • Bipartite rigidity. Trans. Amer. Math. Soc
Call the resulting graph H. The induced subgraph of H on the 3 red vertices v 1 , v 2 , v 34 and the 3 blue vertices v 3
  • Call the resulting graph H. The induced subgraph of H on the 3 red vertices v 1 , v 2 , v 34 and the 3 blue vertices v 3
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