DeepAI AI Chat
Log In Sign Up

Partitioning edges of a planar graph into linear forests and a matching

by   Marthe Bonamy, et al.

We show that the edges of any planar graph of maximum degree at most 9 can be partitioned into 4 linear forests and a matching. Combined with known results, this implies that the edges of any planar graph G of odd maximum degree Δ≥ 9 can be partitioned into Δ-12 linear forests and one matching. This strengthens well-known results stating that graphs in this class have chromatic index Δ [Vizing, 1965] and linear arboricity at most ⌈(Δ+1)/2⌉ [Wu, 1999].


page 1

page 2

page 3

page 4


Vertex partitions of (C_3,C_4,C_6)-free planar graphs

A graph is (k_1,k_2)-colorable if its vertex set can be partitioned into...

Decomposing 4-connected planar triangulations into two trees and one path

Refining a classical proof of Whitney, we show that any 4-connected plan...

Tree-like distance colouring for planar graphs of sufficient girth

Given a multigraph G and a positive integer t, the distance-t chromatic ...

Induced and Weak Induced Arboricities

We define the induced arboricity of a graph G, denoted by ia(G), as the...

Some Results on Dominating Induced Matchings

Let G be a graph, a dominating induced matching (DIM) of G is an induced...

Equitable partition of graphs into induced linear forests

It is proved that the vertex set of any simple graph G can be equitably ...

Partitioning sparse graphs into an independent set and a graph with bounded size components

We study the problem of partitioning the vertex set of a given graph so ...