Research PaperNo Access

Fractional DP-chromatic number of planar graphs of large girth

Jianglin Wu

Department of Mathematics, Zhejiang Normal University, P. R. China

https://doi.org/10.1142/S1793830921501111Cited by:0 (Source: Crossref)

Abstract

This paper proves that for any integer $k \geq 1$ $k \geq 1$ , every planar graph $G$ $G$ of girth at least $8 k - 3$ $8 k - 3$ has fractional DP-chromatic number at most $2 + \frac{1}{k}$ $2 + \frac{1}{k}$ .

Keywords:

AMSC: 05C15

References

1. N. Alon, Z. Tuza and M. Voigt , Choosability and fractional chromatic numbers, Discrete Math. 165–166 (1997) 31–38. Crossref, Google Scholar
2. A. Bernshteyn, A. Kostochka and X. Zhu, Fractional DP-coloring of sparse graphs, preprint (2019), arXiv:1801.07307. Google Scholar
3. Z. Dvořák, X. Hu and H.-S. Sereni, A 4-choosable graph that is not (8:2)-choosable, preprint (2018), arXiv:1806.03880. Google Scholar
4. Z. Dvořk and L. Postle , Correspondence coloring and its application to list-coloring planar graphs without cycles of lengths 4 to 8, J. Combin. Theory Ser. B 129 (2018) 38–54. Crossref, Google Scholar
5. P. Erdős, A. L. Rubin and H. Taylor , Choosability in graphs, Congress. Numer. 26 (1979) 125–127. Google Scholar
6. H. Kaul and J. Mudrock, A note on fractional DP-coloring of graphs, preprint (2019), arXiv:1904.07697. Google Scholar
7. Z. Tuza and M. Voigt , Every 2-choosable graph is (2m, m)-choosable, J. Graph Theory 22 (1996) 245–252. Crossref, Google Scholar
8. X. Zhu , Circular chromatic number of planar graphs of large odd girth, Electron. J. Combin. 8(1) (2001). Crossref, Google Scholar