Bipartite minors

  title={Bipartite minors},
  author={M. Chudnovsky and G. Kalai and Eran Nevo and I. Novik and P. Seymour},
  journal={J. Comb. Theory, Ser. B},
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
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
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
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
These minors preserve Eulerian and even-face properties of ribbon graphs, respectively, and are then characterized using these minors. Expand


Bipartite Rigidity
We develop a bipartite rigidity theory for bipartite graphs parallel to the classical rigidity theory for general graphs, and define for two positive integers k, l the notions of (k, l)-rigid and (k,Expand
Graph Theory
Gaph Teory Fourth Edition is standard textbook of modern graph theory which covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each chapter by one or two deeper results. Expand
On graphs and rigidity of plane skeletal structures
SummaryIn this paper the combinatorial properties of rigid plane skeletal structures are investigated. Those properties are found to be adequately described by a class of graphs.
Planar Permutation Graphs
© Gauthier-Villars, 1967, tous droits réservés. L’accès aux archives de la revue « Annales de l’I. H. P., section B » ( implique l’accord avec les conditionsExpand
Graph theory, volume 173 of Graduate Texts in Mathematics
  • 2000
Über eine Eigenschaft der ebenen Komplexe
*) Z ∪ Y s is critical
  • *) Z ∪ Y s is critical
10*) Z ∪ Y s is critical
  • 10*) Z ∪ Y s is critical
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