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 =
Some results on linear arboricity
β Scribed by Filip Guldan
- Publisher
- John Wiley and Sons
- Year
- 1986
- Tongue
- English
- Weight
- 194 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0364-9024
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π SIMILAR VOLUMES
## 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
## 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.
A digraph G = (V, E) is primitive if, for some positive integer k, there is a u β v walk of length k for every pair u, v of vertices of V . The minimum such k is called the exponent of G, denoted exp(G). The exponent of a vertex u β V , denoted exp(u), is the least integer k such that there is a u β