## Abstract The linear vertexβarboricity Ο(__G__) of a graph __G__ is defined to be the minimum number of subsets into which the vertex set of __G__ can be partitioned such that each subset induces a linear forest. In this paper, we give the sharp upper and lower bounds for the sum and product of l
On the linear vertex-arboricity of a planar graph
β Scribed by K. S. Poh
- Publisher
- John Wiley and Sons
- Year
- 1990
- Tongue
- English
- Weight
- 153 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0364-9024
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β¦ Synopsis
Abstract
We prove in this note that the linear vertexβarboricity of any planar graph is at most three, which confirms a conjecture due to Broere and Mynhardt, and others.
π SIMILAR VOLUMES
The linear arboricity la(G) of a graph G is the minimum number of linear forests that partition the edges of G. Akiyama, Exoo, and Harary conjectured for any simple graph G with maximum degree β. The conjecture has been proved to be true for graphs having β =
## Abstract The linear arboricity of a graph __G__ is the minimum number of linear forests which partition the edges of __G__. Akiyama et al. conjectured that $\lceil {\Delta {({G})}\over {2}}\rceil \leq {la}({G}) \leq \lceil {\Delta({G})+{1}\over {2}}\rceil$ for any simple graph __G__. Wu wu prove
Let G be a planar graph. The vertex face total chromatic number ,y13(G) of G is the least number of colors assigned to V(G) U F(G) such that no adjacent or incident elements receive the same color. The main results of this paper are as follows: (1) We give the vertex face total chromatic number for