Timeline for An inequality on the number of vertex colorings of planar graphs
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Oct 27, 2021 at 7:52 | comment | added | Thomas Lesgourgues | For information, the conjecture is true for all graph $G$ on at most 10 vertices. | |
| Oct 27, 2021 at 7:49 | history | edited | Thomas Lesgourgues | CC BY-SA 4.0 |
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| Oct 27, 2021 at 7:47 | comment | added | Martin Weidner | I like your generalization to ${\rm deg}(v)=d>4$, it looks plausible. The requirement of maximality of the graph can potentially also be relaxed. | |
| Oct 27, 2021 at 7:47 | comment | added | Thomas Lesgourgues | No problem! I'll look at it with fresh eyes now ^^ I'll edit the answer to note that the question has been changed. | |
| Oct 27, 2021 at 7:44 | comment | added | Martin Weidner | I edited the post now to stay "If the minimal degree of 𝐺 is smaller than five,..." to avoid similar confusion in the future. Sorry about this mistake. | |
| Oct 27, 2021 at 7:38 | comment | added | Martin Weidner | Thank you for your reply. Indeed, instead of writing "If the maximal degree of 𝐺 is smaller than four, ..." I should have written "If the minimal degree of $G$ is smaller than five, ..." These are not the same statements, as you point out correctly. However, the claim regarding the four-color theorem is valid. For example, if there is a degree 3 vertex in the minimal counterexample we can just remove that vertex and the resulting graph should still be a counterexample. For degrees $\leq 4$ these are the arguments by Kempe from the 19th century. | |
| Oct 27, 2021 at 7:18 | history | edited | Thomas Lesgourgues | CC BY-SA 4.0 |
Adding conjecture
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| Oct 27, 2021 at 7:05 | history | edited | Thomas Lesgourgues | CC BY-SA 4.0 |
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| Oct 27, 2021 at 6:59 | history | edited | Thomas Lesgourgues | CC BY-SA 4.0 |
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| Oct 27, 2021 at 6:26 | history | answered | Thomas Lesgourgues | CC BY-SA 4.0 |