Author:
Zhou Xiaoling, ,Yang Chao,He Weihua,
Abstract
<abstract><p>A linear $ k $-diforest is a directed forest in which every connected component is a directed path of length at most $ k $. The linear $ k $-arboricity of a digraph $ D $ is the minimum number of linear $ k $-diforests needed to partition the arcs of $ D $. In this paper, we study the linear $ k $-arboricity for digraphs, and determine the linear $ 3 $-arboricity and linear $ 2 $-arboricity for symmetric complete digraphs and symmetric complete bipartite digraphs.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference22 articles.
1. J. Akiyama, G. Exoo, F. Harary, Covering and packing in graphs Ⅲ: Cyclic and acyclic invariants, Math. Slovaca, 30 (1980), 405–417.
2. N. Alon, Probabilistic methods in coloring and decomposition problems, Discrete Math., 127 (1994), 31–46. https://doi.org/10.1016/0012-365X(92)00465-4
3. N. Alon, V. J. Teague, N. C. Wormald, Linear arboricity and linear k-arboricity of regular graphs, Graph. Combinator., 17 (2001), 11–16. https://doi.org/10.1007/PL00007233
4. B. Alspach, J. C. Bermond, D. Sotteau, Decomposition into cycles I: Hamilton decompositions, In: G. Hahn, G. Sabidussi, R. E. Woodrow, Cycles and rays, Dordrecht: Springer, 1990, 9–18. https://doi.org/10.1007/978-94-009-0517-7
5. R. D. Baker, R. M. Wilson, Nearly Kirkman triple systems, Utilitas Math., 11 (1977), 289–296.