The linear arboricity of planar graphs with maximum degree at least 5

نویسندگان

Hong-Yu Chen

Jian-Ming Qi

چکیده

Let G be a planar graph with maximum degree ∆ ≥ 5. It is proved that la(G) = d∆(G)/2e if (1) any 4-cycle is not adjacent to an i-cycle for any i ∈ {3, 4, 5} or (2) G has no intersecting 4-cycles and intersecting i-cycles for some i ∈ {3, 6}. 2010 Mathematics Subject Classification: 05C15

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The 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 کامل

The 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 کامل

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 کامل