A short proof is given of the fact that every graph has an interval representation of depth 2 in which each vertex u is represented by at most &f(u) + 11 intervals, except for an arbitrarily specified vertex w that appears left-most in the representation and is represented by at most [&d(w) + 1)1 in
A bound for the degree of nonholonomy in the plane
β Scribed by Jean-Jacques Risler
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 482 KB
- Volume
- 157
- Category
- Article
- ISSN
- 0304-3975
No coin nor oath required. For personal study only.
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## Abstract Let __C__ be a longest cycle in the 3βconnected graph __G__ and let __H__ be a component of __G__βββ__V__(__C__) such that |__V__(__H__)|ββ₯β3. We supply estimates of the form |__C__|ββ₯β2__d__(__u__)β+β2__d__(__v__)βββΞ±(4ββ€βΞ±ββ€β8), where __u__,__v__ are suitably chosen nonβadjacent verti