We develop a bipartite rigidity theory for bipartite graphs parallel to the classical rigidity theory for general graphs. This theory coincides with the study of Babson–Novik’s balanced shifting restricted to graphs. We establish bipartite analogs of the cone, contraction, deletion, and gluing lemmas, and apply these results to derive a bipartite analog of the rigidity criterion for planar graphs. Our result asserts that a bipartite graph is planar only if its balanced shifting does not contain K3, 3. We also discuss potential applications of this theory to Jockusch’s cubical lower bound conjecture and to upper bound conjectures for embedded simplicial complexes.
|Original language||American English|
|Title of host publication||Springer INdAM Series|
|Publisher||Springer International Publishing|
|Number of pages||8|
|State||Published - 2015|
|Name||Springer INdAM Series|
Bibliographical noteFunding Information:
Research was partially supported by Marie Curie grant IRG-270923 and ISF
© Springer International Publishing Switzerland 2015.