scholarly journals Strong List Edge Coloring of Subcubic Graphs

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Hongping Ma ◽  
Zhengke Miao ◽  
Hong Zhu ◽  
Jianhua Zhang ◽  
Rong Luo
Keyword(s):  
Edge Coloring ◽  
Average Degree ◽  
Maximum Average Degree ◽  
Subcubic Graph ◽  
List Edge Coloring ◽  
Subcubic Graphs

We study strong list edge coloring of subcubic graphs, and we prove that every subcubic graph with maximum average degree less than 15/7, 27/11, 13/5, and 36/13 can be strongly list edge colored with six, seven, eight, and nine colors, respectively.

scholarly journals On strong list edge coloring of subcubic graphs

2014 ◽  
Vol 333 ◽  
pp. 6-13 ◽  
Author(s):  
Hong Zhu ◽  
Zhengke Miao
Keyword(s):  
Edge Coloring ◽  
List Edge Coloring ◽  
Subcubic Graphs

scholarly journals COLORING ALGORITHMS ON SUBCUBIC GRAPHS

2004 ◽  
Vol 15 (01) ◽  
pp. 21-40 ◽  
Author(s):  
SAN SKULRATTANAKULCHAI ◽  
HAROLD N. GABOW
Keyword(s):  
Maximum Degree ◽  
Linear Time ◽  
Edge Coloring ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
The Third ◽  
Erew Pram ◽  
List Edge Coloring ◽  
Subcubic Graphs ◽  
Decomposition Principle

We present efficient algorithms for three coloring problems on subcubic graphs. (A subcubic graph has maximum degree at most three.) The first algorithm is for 4-edge coloring, or more generally, 4-list-edge coloring. Our algorithm runs in linear time, and appears to be simpler than previous ones. The second algorithm is the first randomized EREW PRAM algorithm for the same problem. It uses O(n/ log n) processors and runs in O( log n) time with high probability, where n is the number of vertices of the graph. The third algorithm is the first linear-time algorithm to 5-total-color subcubic graphs. The fourth algorithm generalizes this to get the first linear-time algorithm to 5-list-total-color subcubic graphs. Our sequential algorithms are based on a method of ordering the vertices and edges by traversing a spanning tree of a graph in a bottom-up fashion. Our parallel algorithm is based on a simple decomposition principle for subcubic graphs.

Injective edge-coloring of subcubic graphs

2021 ◽  
Author(s):  
Baya Ferdjallah ◽  
Samia Kerdjoudj ◽  
André Raspaud
Keyword(s):  
Edge Coloring ◽  
Upper Bounds ◽  
Chromatic Index ◽  
Radio Network ◽  
Outerplanar Graphs ◽  
Maximum Average Degree ◽  
Injective Coloring ◽  
Packet Radio Network ◽  
Minimum Integer ◽  
Subcubic Graphs

An injective edge-coloring [Formula: see text] of a graph [Formula: see text] is an edge-coloring such that if [Formula: see text], [Formula: see text], and [Formula: see text] are three consecutive edges in [Formula: see text] (they are consecutive if they form a path or a cycle of length three), then [Formula: see text] and [Formula: see text] receive different colors. The minimum integer [Formula: see text] such that, [Formula: see text] has an injective edge-coloring with [Formula: see text] colors, is called the injective chromatic index of [Formula: see text] ([Formula: see text]). This parameter was introduced by Cardoso et al. [Injective coloring of graphs, Filomat 33(19) (2019) 6411–6423, arXiv:1510.02626] motivated by the Packet Radio Network problem. They proved that computing [Formula: see text] of a graph [Formula: see text] is NP-hard. We give new upper bounds for this parameter and we present the relationships of the injective edge-coloring with other colorings of graphs. We study the injective edge-coloring of some classes of subcubic graphs. We prove that a subcubic bipartite graph has an injective chromatic index bounded by [Formula: see text]. We also prove that if [Formula: see text] is a subcubic graph with maximum average degree less than [Formula: see text] (respectively, [Formula: see text]), then [Formula: see text] admits an injective edge-coloring with at most 4 (respectively, [Formula: see text]) colors. Moreover, we establish a tight upper bound for subcubic outerplanar graphs.

Injective edge coloring of sparse graphs

2018 ◽  
Vol 10 (02) ◽  
pp. 1850022
Author(s):  
Yuehua Bu ◽  
Chentao Qi
Keyword(s):  
Upper Bound ◽  
Edge Coloring ◽  
Average Degree ◽  
Sparse Graphs ◽  
Maximum Average Degree ◽  
Coloring Number

A [Formula: see text]-injective edge coloring of a graph [Formula: see text] is a coloring [Formula: see text], such that if [Formula: see text], [Formula: see text] and [Formula: see text] are consecutive edges in [Formula: see text], then [Formula: see text]. [Formula: see text] has a [Formula: see text]-injective edge coloring[Formula: see text] is called the injective edge coloring number. In this paper, we consider the upper bound of [Formula: see text] in terms of the maximum average degree mad[Formula: see text], where [Formula: see text].

scholarly journals Efficiently list-edge coloring multigraphs asymptotically optimally

2020 ◽  
pp. 2319-2336 ◽  
Author(s):  
Fotis Iliopoulos ◽  
Alistair Sinclair
Keyword(s):  
Edge Coloring ◽  
List Edge Coloring

scholarly journals List Edge Coloring of Outer-1-planar Graphs

2020 ◽  
Vol 36 (3) ◽  
pp. 737-752
Author(s):  
Xin Zhang
Keyword(s):  
Planar Graphs ◽  
Edge Coloring ◽  
List Edge Coloring

scholarly journals Total weight choosability of graphs with bounded maximum average degree

2017 ◽  
Vol 340 (8) ◽  
pp. 2033-2042 ◽  
Author(s):  
Yunfang Tang ◽  
Xuding Zhu
Keyword(s):  
Average Degree ◽  
Total Weight ◽  
Maximum Average Degree

scholarly journals Equitable coloring and equitable choosability of graphs with small maximum average degree

2018 ◽  
Vol 38 (3) ◽  
pp. 829
Author(s):  
Aijun Dong ◽  
Xin Zhang
Keyword(s):  
Average Degree ◽  
Maximum Average Degree ◽  
Equitable Coloring

scholarly journals The Complexity of (List) Edge-Coloring Reconfiguration Problem

2017 ◽  
pp. 347-358 ◽  
Author(s):  
Hiroki Osawa ◽  
Akira Suzuki ◽  
Takehiro Ito ◽  
Xiao Zhou
Keyword(s):  
Edge Coloring ◽  
List Edge Coloring

scholarly journals Coloring the square of graphs whose maximum average degree is less than 4

2016 ◽  
Vol 339 (4) ◽  
pp. 1251-1260 ◽  
Author(s):  
Seog-Jin Kim ◽  
Boram Park
Keyword(s):  
Average Degree ◽  
Maximum Average Degree
Sign in / Sign up

Export Citation Format

Share Document