On disjoint crossing families in geometric graphs
β Scribed by Radoslav Fulek; Andrew Suk
- Book ID
- 119236582
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 190 KB
- Volume
- 38
- Category
- Article
- ISSN
- 1571-0653
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π SIMILAR VOLUMES
We consider the standard random geometric graph process in which n vertices are placed at random on the unit square and edges are sequentially added in increasing order of edge-length. For fixed k β₯ 1, we prove that the first edge in the process that creates a k-connected graph coincides a.a.s. with
## Abstract For a graph __A__ and a positive integer __n__, let __nA__ denote the union of __n__ disjoint copies of __A__; similarly, the union of β΅~0~ disjoint copies of __A__ is referred to as β΅~0~__A__. It is shown that there exist (connected) graphs __A__ and __G__ such that __nA__ is a minor o