The linear 2-arboricity of sparse graphs

Yuanchao Li; Xiaoxue Hu

doi:10.1142/s1793830917500471

The linear 2-arboricity of sparse graphs

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830917500471 ◽

2017 ◽

Vol 09 (04) ◽

pp. 1750047 ◽

Cited By ~ 2

Author(s):

Yuanchao Li ◽

Xiaoxue Hu

Keyword(s):

Sparse Graphs ◽

Edge Disjoint ◽

Linear Formula

The linear [Formula: see text]-arboricity [Formula: see text] of a graph [Formula: see text] is the least integer [Formula: see text] such that [Formula: see text] can be partitioned into [Formula: see text] edge-disjoint forests, whose components are paths of length at most 2. In this paper, we study the linear [Formula: see text]-arboricity of sparse graphs, and prove the following results: (1) let [Formula: see text] be a 2-degenerate graph, we have [Formula: see text]; (2) if [Formula: see text], then [Formula: see text]; (3) if [Formula: see text], then [Formula: see text]; (4) if [Formula: see text], then [Formula: see text]; (5) if [Formula: see text], then [Formula: see text].

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Pebble Game Algorithms and (k,l)-Sparse Graphs

Discrete Mathematics & Theoretical Computer Science ◽

10.46298/dmtcs.3394 ◽

2005 ◽

Vol DMTCS Proceedings vol. AE,... (Proceedings) ◽

Author(s):

Audrey Lee ◽

Ileana Streinu

Keyword(s):

Efficient Algorithms ◽

Sparse Graphs ◽

Edge Disjoint ◽

International Audience ◽

Tree Decompositions ◽

Pebble Game

International audience A multi-graph $G$ on n vertices is $(k,l)$-sparse if every subset of $n'≤n$ vertices spans at most $kn'-l$ edges, $0 ≤l < 2k$. $G$ is tight if, in addition, it has exactly $kn - l$ edges. We characterize $(k,l)$-sparse graphs via a family of simple, elegant and efficient algorithms called the $(k,l)$-pebble games. As applications, we use the pebble games for computing components (maximal tight subgraphs) in sparse graphs, to obtain inductive (Henneberg) constructions, and, when $l=k$, edge-disjoint tree decompositions.

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Linear list r-hued coloring of sparse graphs

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830918500453 ◽

2018 ◽

Vol 10 (04) ◽

pp. 1850045

Author(s):

Hongping Ma ◽

Xiaoxue Hu ◽

Jiangxu Kong ◽

Murong Xu

Keyword(s):

Chromatic Number ◽

Maximum Degree ◽

Average Degree ◽

Disjoint Paths ◽

Proper Coloring ◽

Sparse Graphs ◽

Maximum Average Degree ◽

Linear Formula ◽

Linear List

An [Formula: see text]-hued coloring is a proper coloring such that the number of colors used by the neighbors of [Formula: see text] is at least [Formula: see text]. A linear [Formula: see text]-hued coloring is an [Formula: see text]-hued coloring such that each pair of color classes induces a union of disjoint paths. We study the linear list [Formula: see text]-hued chromatic number, denoted by [Formula: see text], of sparse graphs. It is clear that any graph [Formula: see text] with maximum degree [Formula: see text] satisfies [Formula: see text]. Let [Formula: see text] be the maximum average degree of a graph [Formula: see text]. In this paper, we obtain the following results: (1) If [Formula: see text], then [Formula: see text] (2) If [Formula: see text], then [Formula: see text]. (3) If [Formula: see text], then [Formula: see text].

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Variability of radiosonde-observed precipitable water in the Baltic region*

Hydrology Research ◽

10.2166/nh.2005.0032 ◽

2005 ◽

Vol 36 (4-5) ◽

pp. 423-433 ◽

Cited By ~ 2

Author(s):

E. Jakobson ◽

H. Ohvril ◽

O. Okulov ◽

N. Laulainen

Keyword(s):

Water Vapour ◽

Precipitable Water ◽

Linear Functions ◽

Water Vapour Pressure ◽

Baltic Region ◽

Geographical Latitude ◽

Linear Formula ◽

Annual Means ◽

The Baltic ◽

Two Parameters

The total mass of columnar water vapour (precipitable water, W) is an important parameter of atmospheric thermodynamic and radiative models. In this work more than 60 000 radiosonde observations from 17 aerological stations in the Baltic region over 14 years, 1989–2002, were used to examine the variability of precipitable water. A table of monthly and annual means of W for the stations is given. Seasonal means of W are expressed as linear functions of the geographical latitude degree. A linear formula is also derived for parametrisation of precipitable water as a function of two parameters – geographical latitude and surface water vapour pressure.

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