The List Linear Arboricity of Planar Graphs
نویسندگان
چکیده
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}. We also prove that d 2 e 6 lla(G) 6 d ∆(G)+1 2 e for any planar graph having ∆ > 9.
منابع مشابه
The structure of plane graphs with independent crossings and its applications to coloring problems
If a graph G has a drawing in the plane in such a way that every two crossings are independent, then we call G a plane graph with independent crossings or IC-planar graph for short. In this paper, the structure of IC-planar graphs with minimum degree at least two or three is studied. By applying their structural results, we prove that the edge chromatic number of G is ∆ if ∆ ≥ 8, the list edge ...
متن کاملOn list vertex 2-arboricity of toroidal graphs without cycles of specific length
The vertex arboricity $rho(G)$ of a graph $G$ is the minimum number of subsets into which the vertex set $V(G)$ can be partitioned so that each subset induces an acyclic graph. A graph $G$ is called list vertex $k$-arborable if for any set $L(v)$ of cardinality at least $k$ at each vertex $v$ of $G$, one can choose a color for each $v$ from its list $L(v)$ so that the subgraph induced by ev...
متن کاملThe Linear Arboricity of Planar Graphs without 5-, 6-Cycles with Chords
The linear arboricity la(G) of a graph G is the minimum number of linear forests which partition the edges of G. In this paper, it is proved that for a planar graph G with maximum degree ∆(G) ≥ 7, la(G) = d 2 e if G has no 5-cycles with chords.
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 کاملOn the Linear Arboricity of 1 - Planar Graphs ∗
It is proved that the linear arboricity of every 1-planar graph with maximum degree ∆ > 33 is ⌈∆/2⌉.
متن کامل