The 4-girth-thickness ?$\theta(4, G)$? of a graph ?$G$? is the minimum number of planar subgraphs of girth at least four whose union is ?$G$?. In this paper, we obtain that the 4-girth-thickness of complete tripartite graph ?$K_{n, n, n}$? is ?$\lceil\frac{n + 1}{2}\rceil$? except for ?$\theta(4, K_{1, 1, 1}) = 2$?. And we also show that the 4-girth-thickness of the complete graph ?$K_{10}$? is three which disprove the conjecture posed by C. Rubio-Montiel Ars Math. Contemp. 14, No. 2, 319--327 (2018) concerning to ?$\theta(4, K_{10})$?.

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URN

URN:NBN:SI:DOC-9Y1AWR1R

COBISSID

18699353

Added

29.05.2020

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Citation

APA:

Guo, Xia, Yang, Yan (2019). A note on the 4-girth-thickness of Ksub{n,n,n}. Ars mathematica contemporanea, volume 16, issue 1, str. 19-24. URN:NBN:SI:DOC-9Y1AWR1R from http://www.dlib.si

MLA:

Guo, Xia, Yang, Yan. "A note on the 4-girth-thickness of Ksub{n,n,n}." Ars mathematica contemporanea volume 16. issue 1 (2019) str. 19-24.
<http://www.dlib.si/?URN=URN:NBN:SI:DOC-9Y1AWR1R>

Ars mathematica contemporanea
2008-
(Assembly record)