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

2018 ◽  
Vol E101.A (1) ◽  
pp. 232-238 ◽  
Author(s):  
Hiroki OSAWA ◽  
Akira SUZUKI ◽  
Takehiro ITO ◽  
Xiao ZHOU
Keyword(s):  
Edge Coloring ◽  
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

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.

scholarly journals Planar graphs with $\Delta \geq 7$ and no triangle adjacent to a $C_4$ are minimally edge and total choosable

2016 ◽  
Vol Vol. 17 no. 3 (Graph Theory) ◽  
Author(s):  
Marthe Bonamy ◽  
Benjamin Lévêque ◽  
Alexandre Pinlou
Keyword(s):  
Planar Graphs ◽  
Maximum Degree ◽  
Edge Coloring ◽  
Total Coloring ◽  
List Total Coloring ◽  
List Edge Coloring ◽  
International Audience

International audience For planar graphs, we consider the problems of <i>list edge coloring</i> and <i>list total coloring</i>. Edge coloring is the problem of coloring the edges while ensuring that two edges that are adjacent receive different colors. Total coloring is the problem of coloring the edges and the vertices while ensuring that two edges that are adjacent, two vertices that are adjacent, or a vertex and an edge that are incident receive different colors. In their list extensions, instead of having the same set of colors for the whole graph, every vertex or edge is assigned some set of colors and has to be colored from it. A graph is minimally edge or total choosable if it is list $\Delta$-edge-colorable or list $(\Delta +1)$-total-colorable, respectively, where $\Delta$ is the maximum degree in the graph. It is already known that planar graphs with $\Delta \geq 8$ and no triangle adjacent to a $C_4$ are minimally edge and total choosable (Li Xu 2011), and that planar graphs with $\Delta \geq 7$ and no triangle sharing a vertex with a $C_4$ or no triangle adjacent to a $C_k (\forall 3 \leq k \leq 6)$ are minimally total colorable (Wang Wu 2011). We strengthen here these results and prove that planar graphs with $\Delta \geq 7$ and no triangle adjacent to a $C_4$ are minimally edge and total choosable.

Optimal channel assignment with list-edge coloring

2019 ◽  
Vol 38 (1) ◽  
pp. 197-207 ◽  
Author(s):  
Huijuan Wang ◽  
Panos M. Pardalos ◽  
Bin Liu
Keyword(s):  
Channel Assignment ◽  
Edge Coloring ◽  
List Edge Coloring

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 List edge coloring of planar graphs without 6-cycles with two chords

2021 ◽  
Vol 41 (1) ◽  
pp. 199
Author(s):  
Linna Hu ◽  
Lei Sun ◽  
Jian-Liang Wu
Keyword(s):  
Planar Graphs ◽  
Edge Coloring ◽  
List Edge Coloring
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