Bipartite rigidity

Eran Nevo*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-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 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 languageAmerican English
Title of host publicationSpringer INdAM Series
PublisherSpringer International Publishing
Pages107-114
Number of pages8
DOIs
StatePublished - 2015

Publication series

NameSpringer INdAM Series
Volume12
ISSN (Print)2281-518X
ISSN (Electronic)2281-5198

Bibliographical note

Publisher Copyright:
© Springer International Publishing Switzerland 2015.

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