منابع مشابه
Some structural results on linear arboricity
A linear forest-factor F of a graph G is a spanning subgraph of G whose components are paths. A linear forest-decomposition of G is a collection :F = {F1, ••• , Fk } of linear forest-factors of G such that the edge set E (G) of G is the disjoint union of E (F1), •.• , E (Fk)' The linear ar borici ty la( G) of G is the minimum cardinality of a linear forest-decomposition of G. In this paper we e...
متن کاملLinear Arboricity and Linear k-Arboricity of Regular Graphs
We find upper bounds on the linear k-arboricity of d-regular graphs using a probabilistic argument. For small k these bounds are new. For large k they blend into the known upper bounds on the linear arboricity of regular graphs.
متن کاملA Planar Linear Arboricity Conjecture
The linear arboricity la(G) of a graph G is the minimum number of linear forests (graphs where every connected component is a path) that partition the edges of G. In 1984, Akiyama et al. [1] stated the Linear Arboricity Conjecture (LAC), that the linear arboricity of any simple graph of maximum degree ∆ is either ⌈ ∆ 2 ⌉
متن کاملThe Linear Arboricity of Graphs
A linear forest is a forest in which each connected component is a path. The linear arboricity la(G) of a graph G is the minimum number of linear forests whose union is the set of all edges of G. The linear arboricity conjecture asserts that for every simple graph G with maximum degree A = A(G), Although this conjecture received a considerable amount of attention, it has been proved only for A ...
متن کاملSome Linear Algebra Problems SOLUTIONS
Most of these problems were written for my students in Math 23a/b at Harvard in 2011/2012 and 2012/2013.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1982
ISSN: 0012-365X
DOI: 10.1016/0012-365x(82)90209-6