We show that one can choose the minimum degree of a k-connected graph G large enough (independent of the vertex number of G) such that G contains a copy T of a prescribed tree with the property that G -V (T ) remains k-connected.
Rainbow trees in graphs and generalized connectivity
β Scribed by Gary Chartrand; Futaba Okamoto; Ping Zhang
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 145 KB
- Volume
- 55
- Category
- Article
- ISSN
- 0028-3045
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let G = ( V , A ) be a digraph with diameter D # 1. For a given integer 2 5 t 5 D , the t-distance connectivity K ( t ) of G is the minimum cardinality of an z --+ y separating set over all the pairs of vertices z, y which are a t distance d(z, y) 2 t. The t-distance edge connectivity X ( t ) of G i
## Abstract We study vertexβcolorings of plane graphs that do not contain a rainbow face, i.e., a face with vertices of mutually distinct colors. If __G__ is a 3 βconnected plane graph with __n__ vertices, then the number of colors in such a coloring does not exceed $\lfloor{{7n-8}\over {9}}\rfloo
A generalized x-parking function associated to a positive integer vector of the form a b b b is a sequence a 1 a 2 a n of positive integers whose The set of x-parking functions has the same cardinality as the set of sequences of rooted b-forests on n . We construct a bijection between these two set