On the linear arboricity of planar graphs
نویسنده
چکیده
It is proved that the linear arboricity of every 1-planar graph with maximum degree ∆ > 33 is ⌈∆/2⌉.
منابع مشابه
On 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 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 کاملA Note on The Linear Arboricity of Planar Graphs without 4-Cycles∗
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 if G is a planar graph with ∆(G) ≥ 5 and without 4-cycles, then la(G) = ⌈∆(G) 2 ⌉. Moreover, the bound that ∆(G)≥ 5 is sharp.
متن کاملThe Linear Arboricity of Planar Graphs without 5-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(∆(G))/2e if G has no 5-cycles with chords. 2010 Mathematics Subject Classification: 05C15
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}....
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عنوان ژورنال:
- Journal of Graph Theory
دوره 31 شماره
صفحات -
تاریخ انتشار 1999