For graphs G and H, let G× H denote their categorical product and let chi(G) denote the chromatic number of a graph. Hedetniemi's conjecture. chi(G× H)=minchi(G),chi(H). This is a famous open problem in graph theory concerning how chromatic number behaves under categorical products.

Hedetniemi's conjecture on the chromatic number of categorical graph products

About 8 years old · traced to 2018

For graphs $G$ and $H$ , let $G\times H$ denote their categorical product and let $\chi(G)$ denote the chromatic number of a graph. Hedetniemi's conjecture.

\chi(G\times H)=\min\{\chi(G),\chi(H)\}.

This is a famous open problem in graph theory concerning how chromatic number behaves under categorical products.

References

Primary source

Samir Shukla, “Neighborhood complexes, homotopy test graphs and a contribution to a conjecture of Hedetniemi”, arXiv:1810.00648 (2018).

Additional references

6 papers in this index state this conjecture (2012–2018). The statement above is taken from the most recent of them; the others are arXiv:1803.01505, arXiv:1710.05290, arXiv:1608.02918, arXiv:1305.5545, arXiv:1202.5720.

Source: https://arxiv.org/abs/1810.00648 Hedetniemi (year not specified), Hedetniemi's conjecture

graph-coloring graph-products

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