Bipartite rigidity

Eran Nevo

doi:10.1007/978-3-319-20155-9_20

Bipartite rigidity

Eran Nevo^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

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 K_{3, 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	English
Title of host publication	Springer INdAM Series
Publisher	Springer International Publishing
Pages	107-114
Number of pages	8
DOIs	https://doi.org/10.1007/978-3-319-20155-9_20
State	Published - 2015

Publication series

Name	Springer INdAM Series
Volume	12
ISSN (Print)	2281-518X
ISSN (Electronic)	2281-5198

Bibliographical note

Publisher Copyright:
© Springer International Publishing Switzerland 2015.

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10.1007/978-3-319-20155-9_20

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Bipartite rigidity

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