Extending polar spaces of rank at least 3
β Scribed by Dmitrii V Pasechnik
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 557 KB
- Volume
- 72
- Category
- Article
- ISSN
- 0097-3165
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π SIMILAR VOLUMES
Let 2 be a finite thick dual polar space of rank 3. We say that a hyperplane H of 2 is locally singular (respectively, quadrangular or ovoidal) if H & Q is the perp of a point (resp. a subquadrangle or an ovoid) of Q for every quad Q of 2. If H is locally singular, quadrangular, or ovoidal, then we
In this article, we show that all quadrangulations of the sphere with minimum degree at least 3 can be constructed from the pseudo-double wheels, preserving the minimum degree at least 3, by a sequence of two kinds of transformations called "vertex-splitting" and "4-cycle addition." We also consider
It is known that every triangle-free (equivalently, of girth at least 4) circle graph is 5-colourable and that there exist examples of these graphs which are not 4-colourable . In this note we show that every circle graph of girth at least 5 is 2-degenerate and, consequently, not only 3-colourable
## Abstract A point disconnecting set __S__ of a graph __G__ is a nontrivial __m__βseparator, where __m__ = |__S__|, if the connected components of __G__ β __S__ can be partitioned into two subgraphs, each of which has at least two points. A 3βconnected graph is quasi 4βconnected if it has no nontr