Timeline for Extension of chromatic polynomial to multi graphs
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Feb 18, 2022 at 2:34 | comment | added | GA316 | @AaronDall similarly, can we read the number of (multi)edges between two particular vertices $u$ and $v$ of $G$ from $T$? | |
| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| May 16, 2020 at 21:40 | vote | accept | GA316 | ||
| Feb 6, 2019 at 18:28 | comment | added | Fedor Petrov | (cont.) it clearly generalizes the chromatic polynomial and clearly relies on the multiplicities of edges. The connection with Tutte polynomial $T(x, y) $ is via the change of variables $s=y-1,q=(x-1)(y-1)$. $T(x, y) =q^{-r}s^{r-N} Z(q, s) $, where $r$ is the number of connected components and $n$ the number of vertices. | |
| Feb 6, 2019 at 18:21 | comment | added | Fedor Petrov | Alternatively, you may consider the bichromatic polynomial $Z(q, s) =\sum (1+s)^{m}$, where the summation is over all (not only proper) colourings of vertices with $q$ colors, $m$ is the number of not properly colored edges. | |
| Feb 2, 2019 at 8:25 | comment | added | Aaron Dall | The value $T(2,2)$ is $2^n$ where $n$ is the total number of edges in the graph. | |
| Feb 2, 2019 at 6:18 | comment | added | GA316 | Thank you. I have some doubts. Is it possible to extract the number of edges between the vertices from Tutte polynomial? | |
| Feb 1, 2019 at 7:55 | history | answered | Carl-Fredrik Nyberg Brodda | CC BY-SA 4.0 |