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Sep 20, 2023 at 7:13 comment added domotorp @CCC Please edit the question you have posed to make it more clear. For example, you could start with asking for bounds on $\omega$ of an $n$-vertex $k$-critical graph, and then you can give all the definitions and history. It also helps to highlight your main question with the formatting tools.
Sep 19, 2023 at 16:18 comment added CCC Thank you for your answer. Maybe I should be more precise. While we discuss the maximum number of edges in a $k$-critical graph, the number of vertices of this graph should always be fixed, denoted by $n$. When $n=k$, it is trivial. As you said, $K_k$ would be what we want. But when $n$ is strictly larger than $k$, it would be hard. Do you have any idea about the clique number of critical graphs in this case?
Sep 19, 2023 at 10:58 history edited Tony Huynh CC BY-SA 4.0
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Sep 19, 2023 at 10:23 history answered Tony Huynh CC BY-SA 4.0