The linear arboricity of graphs

N Alon - Israel Journal of Mathematics, 1988 - Springer
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 …

Monochromatic and heterochromatic subgraphs in edge-colored graphs-a survey

M Kano, X Li - Graphs and Combinatorics, 2008 - Springer
Nowadays the term monochromatic and heterochromatic (or rainbow, multicolored)
subgraphs of an edge-colored graph appeared frequently in literature, and many results on …

Two-coloring the edges of a cubic graph such that each monochromatic component is a path of length at most 5

C Thomassen - Journal of Combinatorial Theory, Series B, 1999 - Elsevier
Two- Coloring the Edges of a Cubic Graph Such That Each Monochromatic Component Is a
Path of Length at Most 5 Page 1 Journal of Combinatorial Theory, Series B 75, 100 109 (1999) …

[HTML][HTML] Bounded size components—partitions and transversals

P Haxell, T Szabó, G Tardos - Journal of Combinatorial Theory, Series B, 2003 - Elsevier
Answering a question of Alon et al., we show that there exists an absolute constant C such
that every graph G with maximum degree 5 has a vertex partition into 2 parts, such that the …

New lower bounds on the size-Ramsey number of a path

D Bal, L DeBiasio - arXiv preprint arXiv:1909.06354, 2019 - arxiv.org
We prove that for all graphs with at most $(3.75-o (1)) n $ edges there exists a 2-coloring of
the edges such that every monochromatic path has order less than $ n $. This was …

Linear arboricity and linear k-arboricity of regular graphs

N Alon, VJ Teague, NC Wormald - Graphs and Combinatorics, 2001 - Springer
Graphs and Combinatorics Page 1 Linear Arboricity and Linear k-Arboricity of Regular Graphs
Noga Alon1Ãy, VJ Teague2, and NC Wormald3z 1 School of Mathematics, Institute for …

On the linear k-arboricity of cubic graphs

B Jackson, NC Wormald - Discrete Mathematics, 1996 - Elsevier
On the linear k-arboricity of cubic graphs Page 1 DISCRETE MATHEMATICS ELSEVIER
Discrete Mathematics 162 (1996) 293-297 Note On the linear k-arboricity of cubic graphs …

[HTML][HTML] Linear k-arboricities on trees

GJ Chang, BL Chen, HL Fu, KC Huang - Discrete applied mathematics, 2000 - Elsevier
For a fixed positive integer k, the linear k-arboricity lak (G) of a graph G is the minimum
number ℓ such that the edge set E (G) can be partitioned into ℓ disjoint sets and that each …

[PDF][PDF] More on the linear k-arboricity of regular graphs

REL Aldred, NC Wormald - Australasian Journal of Combinatorics, 1998 - Citeseer
Abstract Bermond et al.[5] conjectured that the edge set of a cubic graph G can be
partitioned into two linear k-forests, that is to say two forests whose connected components …

The linear 2-arboricity of planar graphs

KW Lih, LD Tong, WF Wang - Graphs and Combinatorics, 2003 - Springer
Let G be a planar graph with maximum degree Δ and girth g. The linear 2-arboricity la 2 (G)
of G is the least integer k such that G can be partitioned into k edge-disjoint forests, whose …