scholarly journals Acyclic list edge coloring of outerplanar graphs

2013 ◽  
Vol 313 (3) ◽  
pp. 301-311
Author(s):  
Qiaojun Shu ◽  
Yiqiao Wang ◽  
Weifan Wang
Keyword(s):  
Edge Coloring ◽  
Outerplanar Graphs ◽  
List Edge Coloring

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

WEIGHTED-EDGE-COLORING OF k-DEGENERATE GRAPHS AND BIN-PACKING

2011 ◽  
Vol 12 (01n02) ◽  
pp. 109-124
Author(s):  
FLORIAN HUC
Keyword(s):  
Bin Packing ◽  
Edge Coloring ◽  
Weighted Graph ◽  
Packing Problem ◽  
Bipartite Graphs ◽  
Specific Class ◽  
Weighted Graphs ◽  
Outerplanar Graphs ◽  
Underlying Graph ◽  
Multiple Edges

The weighted-edge-coloring problem of an edge-weighted graph whose weights are between 0 and 1, consists in finding a coloring using as few colors as possible and satisfying the following constraints: the sum of weights of edges with the same color and incident to the same vertex must be at most 1. In 1991, Chung and Ross conjectured that if G is bipartite, then [Formula: see text] colors are always sufficient to weighted-edge-color (G,w), where [Formula: see text] is the maximum of the sums of the weights of the edges incident to a vertex. We prove this is true for edge-weighted graphs with multiple edges whose underlying graph is a tree. We further generalise this conjecture to non-bipartite graphs and prove the generalised conjecture for simple edge-weighted outerplanar graphs. Finally, we introduce a list version of this coloring together with the list-bin-packing problem, which allows us to obtain new results concerning the original coloring for a specific class of graphs, namely the k-weight-degenerate weighted graph.

Edge coloring by total labelings of outerplanar graphs

2013 ◽  
Vol 29 (11) ◽  
pp. 2129-2136
Author(s):  
Guang Hui Wang ◽  
Gui Ying Yan
Keyword(s):  
Edge Coloring ◽  
Outerplanar Graphs

scholarly journals Proof of the List Edge Coloring Conjecture for Complete Graphs of Prime Degree

10.37236/4084 ◽  
2014 ◽  
Vol 21 (3) ◽  
Author(s):  
Uwe Schauz
Keyword(s):  
Group Action ◽  
Edge Coloring ◽  
Latin Squares ◽  
Combinatorial Nullstellensatz ◽  
Complete Graphs ◽  
Chromatic Index ◽  
Prime Degree ◽  
List Edge Coloring ◽  
Class 1

We prove that the list-chromatic index and paintability index of $K_{p+1}$ is $p$, for all odd primes $p$. This implies that the List Edge Coloring Conjecture holds for complete graphs with less then 10 vertices. It also shows that there are arbitrarily big complete graphs for which the conjecture holds, even among the complete graphs of class 1. Our proof combines the Quantitative Combinatorial Nullstellensatz with the Paintability Nullstellensatz and a group action on symmetric Latin squares. It displays various ways of using different Nullstellensätze. We also obtain a partial proof of a version of Alon and Tarsi's Conjecture about even and odd Latin squares.

Efficient Vertex- and Edge-Coloring of Outerplanar Graphs

1986 ◽  
Vol 7 (1) ◽  
pp. 131-136 ◽  
Author(s):  
Andrzej Proskurowski ◽  
Maciej M. Sysło
Keyword(s):  
Edge Coloring ◽  
Outerplanar Graphs

A polynomial-time nearly-optimal algorithm for an edge coloring problem in outerplanar graphs

2015 ◽  
Vol 65 (2) ◽  
pp. 351-367 ◽  
Author(s):  
Weifan Wang ◽  
Danjun Huang ◽  
Yanwen Wang ◽  
Yiqiao Wang ◽  
Ding-Zhu Du
Keyword(s):  
Polynomial Time ◽  
Optimal Algorithm ◽  
Edge Coloring ◽  
Outerplanar Graphs ◽  
Coloring Problem

A note on the strong edge-coloring of outerplanar graphs with maximum degree 3

2016 ◽  
Vol 32 (4) ◽  
pp. 883-890
Author(s):  
Shun-yi Liu ◽  
He-ping Zhang ◽  
Hong-liang Lu ◽  
Yu-qing Lin
Keyword(s):  
Maximum Degree ◽  
Edge Coloring ◽  
Outerplanar Graphs
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