![](/files/happy5.png)
Edge coloring
Packing T-joins ★★
Author(s): DeVos
![$ c $](/files/tex/dccee841f3f498c2c58fa6ae1c1403c5a88c5b8d.png)
![$ c=1 $](/files/tex/7a8b9609d823e7ffb81159e3dfcbd5cb2599e11d.png)
![$ T $](/files/tex/79f55d2e1d83a7726c807a70cbe756713b0437b6.png)
![$ k $](/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png)
![$ T $](/files/tex/79f55d2e1d83a7726c807a70cbe756713b0437b6.png)
![$ (2/3)k-c $](/files/tex/da50fbb1472ce7fd6fa00876af3022e1be50d2ec.png)
Acyclic edge-colouring ★★
Author(s): Fiamcik
![$ \Delta $](/files/tex/e3f8e135c571143e94f1d4f236326b862080b200.png)
![$ (\Delta+2) $](/files/tex/6a77f06e08e0a0d164f09aa262634fe605297c08.png)
Keywords: edge-coloring
A generalization of Vizing's Theorem? ★★
Author(s): Rosenfeld
![$ H $](/files/tex/76c7b422c8e228780f70a4f31614cfcf3f831c65.png)
![$ d $](/files/tex/aeba4a4076fc495e8b5df04d874f2911a838883a.png)
![$ d-1 $](/files/tex/377f809b25769f204a72e5d4765cddd8aaabe392.png)
![$ r $](/files/tex/535dee6c3b72bcc4d571239ed00be162ee1e6fbe.png)
![$ r+d-1 $](/files/tex/43f812f49b2b3aee5d87139eaff0e0fe02c47dc8.png)
![$ d-1 $](/files/tex/377f809b25769f204a72e5d4765cddd8aaabe392.png)
Keywords: edge-coloring; hypergraph; Vizing
List colorings of edge-critical graphs ★★
Author(s): Mohar
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ \Delta $](/files/tex/e3f8e135c571143e94f1d4f236326b862080b200.png)
![$ e $](/files/tex/5105762e0c97083905ebf07919c7d4d5ed38dce3.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ L(e) $](/files/tex/bd0dfc00a21966b9e90231c00dab0d0aa81a0ab0.png)
![$ \Delta $](/files/tex/e3f8e135c571143e94f1d4f236326b862080b200.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ L $](/files/tex/73f33398d7e8aa42e6ec25ee2bb4f2b57ed3391a.png)
Keywords: edge-coloring; list coloring
Universal Steiner triple systems ★★
Author(s): Grannell; Griggs; Knor; Skoviera
Keywords: cubic graph; Steiner triple system
Edge list coloring conjecture ★★★
Author(s):
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
Keywords:
Seymour's r-graph conjecture ★★★
Author(s): Seymour
An -graph is an
-regular graph
with the property that
for every
with odd size.
![$ \chi'(G) \le r+1 $](/files/tex/efa38d9230a3451d1c38c061522cb607572d369b.png)
![$ r $](/files/tex/535dee6c3b72bcc4d571239ed00be162ee1e6fbe.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
Keywords: edge-coloring; r-graph
Goldberg's conjecture ★★★
Author(s): Goldberg
The overfull parameter is defined as follows:
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$ \chi'(G) \le \max\{ \Delta(G) + 1, w(G) \} $](/files/tex/688f47d207abb99bb15f8fc2353553cf3904fc1d.png)
Keywords: edge-coloring; multigraph
Strong edge colouring conjecture ★★
A strong edge-colouring of a graph is a edge-colouring in which every colour class is an induced matching; that is, any two vertices belonging to distinct edges with the same colour are not adjacent. The strong chromatic index
is the minimum number of colours in a strong edge-colouring of
.
![$$s\chi'(G) \leq \frac{5\Delta^2}{4}, \text{if $\Delta$ is even,}$$](/files/tex/a63811dfccf4e3128accc3daca7041ff5097e2a2.png)
![$$s\chi'(G) \leq \frac{5\Delta^2-2\Delta +1}{4},&\text{if $\Delta$ is odd.}$$](/files/tex/987d7e1dcf43bb92750a5d1dffe79abc224035c2.png)
Keywords:
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