Combinatorial Methods in Topology and Algebra by Bruno Benedetti Emanuele Delucchi & Luca Moci

Author:Bruno Benedetti, Emanuele Delucchi & Luca Moci
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

We now establish bipartite analogs of the deletion, contraction, gluing and cone lemmas in classical rigidity.

Lemma 1 (Deletion Lemma)

Let G be a bipartite graph, v a vertex of G of degree d, and G′ = G − v the graph obtained from G by deleting v. 1. If G′ is (k,l)-stress free and , then G is (k,l)-stress free.

2. If G′ is (k,l)–rigid and , then G is (k,l)-rigid.

Lemma 2 (Contraction Lemma)

Let G = (V,E) be a bipartite graph, v and w two vertices of G that belong to the same part, C the set of common neighbors of v and w, and G′ = (V −{ v},E′) the graph obtained from G by contracting v with w. 1. If G′ is (k,l)-stress free and , then G is (k,l)-stress free.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.