# Bispindle in strongly connected digraphs with large chromatic number

@article{Cohen2017BispindleIS, title={Bispindle in strongly connected digraphs with large chromatic number}, author={Nathann Cohen and Fr{\'e}d{\'e}ric Havet and William Lochet and Raul Lopes}, journal={Electron. Notes Discret. Math.}, year={2017}, volume={62}, pages={69-74} }

## 2 Citations

### Remarks on the subdivisions of bispindles and two-blocks cycles in highly chromatic digraphs

- Mathematics
- 2020

A $(2+1)$-bispindle $B(k_1,k_2;k_3)$ is the union of two $xy$-dipaths of respective lengths $k_1$ and $k_2$, and one $yx$-dipath of length $k_3$, all these dipaths being pairwise internally disjoint.…

### Sous-structures dans les graphes dirigés

- Philosophy
- 2018

Le but principal de cette these est de presenter des conditions suffisantes pour garantir l'existence de subdivisions dans les graphes diriges. Bien que ce genre de questions soit assez bien maitrise…

## References

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- MathematicsJ. Graph Theory
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This paper is able to find a digraph which shows that the answer to the above problem is no and it is shown that if in addition £D is Hamiltonian, then its underlying simple graph is $(k+\ell-1)$-degenerate and thus the chromatic number of $D$ is at most $k-\ell$, which is tight.

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- MathematicsJ. Graph Theory
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It is shown that for any oriented cycle C, there are digraphs containing no subdivision of $C$ (as a subdigraph) and arbitrarily large chromatic number and for any cycle with two blocks, every strongly connected digraph with sufficiently large Chromatic number contains a subdivision of C.

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