منابع مشابه
The 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 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 کاملOn the linear arboricity of planar graphs
It is proved that the linear arboricity of every 1-planar graph with maximum degree ∆ > 33 is ⌈∆/2⌉.
متن کاملThe List Linear Arboricity of Planar Graphs
The linear arboricity la(G) of a graph G is the minimum number of linear forests which partition the edges of G. An and Wu introduce the notion of list linear arboricity lla(G) of a graph G and conjecture that lla(G) = la(G) for any graph G. We confirm that this conjecture is true for any planar graph having ∆ > 13, or for any planar graph with ∆ > 7 and without i-cycles for some i ∈ {3, 4, 5}....
متن کاملLinear Arboricity of Random Regular Graphs
An easy count ing argument shows here that la(G)>f . f f t " d i f f icu l ty is in establishing the upper bound. This problem has received much attention; see Alon [1]. We show here how Alon's beautiful treatment for graphs with large girth allows us easily to handle random regular graphs. By the random regular graph G,,, (where rn is even) we mean a graph picked uniformly at random from the s...
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 1988
ISSN: 0021-2172,1565-8511
DOI: 10.1007/bf02783300