• Corpus ID: 233025071

# A note on cycle lengths in graphs of chromatic number five and six

@inproceedings{Huo2021ANO,
title={A note on cycle lengths in graphs of chromatic number five and six},
author={Qingyi Huo},
year={2021}
}
In this note, we prove that every non-complete (k+1)-critical graph contains cycles of all lengths modulo k, where k = 4, 5. Together with a result in [7], this completely gives an affirmative answer to the question of Moore and West on graphs of given chromatic number.

## References

SHOWING 1-10 OF 13 REFERENCES
A Strengthening on Odd Cycles in Graphs of Given Chromatic Number
• Mathematics
SIAM Journal on Discrete Mathematics
• 2021
Resolving a conjecture of Bollobás and Erdős, Gyárfás proved that every graph G of chromatic number k + 1 ≥ 3 contains cycles of ⌊ 2 ⌋ distinct odd lengths. We strengthen this prominent result by
A Unified Proof of Conjectures on Cycle Lengths in Graphs
• Mathematics
• 2019
In this paper, we prove a tight minimum degree condition in general graphs for the existence of paths between two given endpoints, whose lengths form a long arithmetic progression with common
Minimum degree conditions for the existence of cycles of all lengths modulo $k$ in graphs
• Mathematics
• 2019
Thomassen, in 1983, conjectured that for a positive integer $k$, every $2$-connected non-bipartite graph of minimum degree at least $k + 1$ contains cycles of all lengths modulo $k$. In this paper,
Graph decomposition with applications to subdivisions and path systems modulo k
The existence of a function α(k) (where k is a natural number) is established such that the vertex set of any graph G has a decomposition A ∪ B ∪ C such that G has minimum degree at least k.
On the distribution of cycle lengths in graphs
• Mathematics
J. Graph Theory
• 1984
Two results are proved indicating that C(G) is dense in some sense, which leads to the solution of a conjecture of Erdos and Hajnal stating that for suitable positive constants a, b the following holds.
Paths
Why should wait for some days to get or receive the paths book that you order? Why should you take it if you can get the faster one? You can find the same book that you order right here. This is it
The Extremal Function for Cycles of Length l mod k
• Mathematics
Electron. J. Comb.
• 2017
It is shown that c_k(\ell) is proportional to the largest average degree of a $C_{\ell}$-free graph on $k$ vertices, which determines $c_k(ell)$ up to an absolute constant.
Cycle lengths and minimum degree of graphs
• Mathematics
J. Comb. Theory, Ser. B
• 2018