Timeline for Does a critical graph have to be product-irreducible?
Current License: CC BY-SA 4.0
9 events
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| Nov 2, 2023 at 14:23 | history | edited | Dominic van der Zypen | CC BY-SA 4.0 |
explanation on $G\setminus\{v\}$
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| Nov 2, 2023 at 10:11 | history | edited | Dominic van der Zypen | CC BY-SA 4.0 |
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| Nov 2, 2023 at 9:27 | comment | added | Emil Jeřábek | @HenrikRüping I believe $\chi(G)$ here denotes the chromatic number rather than the Euler characteristic. | |
| Nov 2, 2023 at 8:35 | comment | added | HenrikRüping | $G\setminus\{v\}$ means removing all adjacent edges as well. If so, since the Euler-characteristic of a graph is the number of vertices minus the number of edges, vertex-cricical just means that at every vertex there are at least to edges. Thus for example $C_3\times C_2 \cong C_6$ is an example. | |
| Nov 2, 2023 at 8:19 | history | edited | Dominic van der Zypen | CC BY-SA 4.0 |
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| Nov 2, 2023 at 8:19 | comment | added | Dominic van der Zypen | @SamHopkins Actually, in the context of the tensor product, you don't need to explicitly exclude the one point graph $G_1$, because $G\times G_1$ is always a graph with no edges (all points are isolated), and vertex-critical graphs are always connected | |
| Nov 2, 2023 at 8:14 | comment | added | Dominic van der Zypen | Thanks - I was thinking of the categorical product of graphs and will put this in the question. Apologies for the ambiguity. | |
| Nov 1, 2023 at 19:07 | comment | added | Sam Hopkins | I think you should specify what product on graphs you are considering here (e.g. en.wikipedia.org/wiki/Cartesian_product_of_graphs or en.wikipedia.org/wiki/Tensor_product_of_graphs or en.wikipedia.org/wiki/Strong_product_of_graphs). Also clearly you mean to assume $H_1$ and $H_2$ have more than one vertex. | |
| Nov 1, 2023 at 16:48 | history | asked | Dominic van der Zypen | CC BY-SA 4.0 |