![](/files/happy5.png)
List colorings of edge-critical graphs
Conjecture Suppose that
is a
-edge-critical graph. Suppose that for each edge
of
, there is a list
of
colors. Then
is
-edge-colorable unless all lists are equal to each other.
![$ 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)
(Reproduced from [M].)
A graph is said to be
-edge-critical if it is not
-edge-colorable but every edge-deleted subgraph is
-edge-colorable. (Here
is the maximum degree of
.)
Bibliography
*[M] B. Mohar, Problem of the Month
* indicates original appearance(s) of problem.