@inbook{0537a49ee82942349e92b3fd8a77d45d,
title = "Bipartite rigidity",
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{\textquoteright}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{\textquoteright}s cubical lower bound conjecture and to upper bound conjectures for embedded simplicial complexes.",
author = "Eran Nevo",
note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2015.",
year = "2015",
month = jan,
day = "1",
doi = "https://doi.org/10.1007/978-3-319-20155-9_20",
language = "الإنجليزيّة",
isbn = "9783319369983",
series = "Springer INdAM Series",
pages = "107--114",
editor = "Bruno Benedetti and Emanuele Delucchi and Luca Moci",
booktitle = "Springer INdAM Series",
}