discharging method
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2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Wenwen Zhang

In this paper, by applying the discharging method, we show that if G is a planar graph with a maximum degree of Δ = 6 that does not contain any adjacent 8-cycles, then G is of class 1.



2020 ◽  
Author(s):  
Kerista Tarigan ◽  
Syahrul Humaidi ◽  
Kurnia Brahmana


2019 ◽  
Vol 31 (3) ◽  
pp. 035302
Author(s):  
Dongmei Wan ◽  
Hengsheng Xiang ◽  
Haitao Xu


2019 ◽  
Vol 55 (5) ◽  
pp. 4846-4854 ◽  
Author(s):  
Jianyu Pan ◽  
Ziwei Ke ◽  
Muneer Al Sabbagh ◽  
Risha Na ◽  
Julia Zhang ◽  
...  


2017 ◽  
Vol 875 ◽  
pp. 112008
Author(s):  
Tokihiro Ikeda ◽  
Takao M. Kojima ◽  
Yoshio Natsume ◽  
Jun Kimura ◽  
Tomoko Abe


2017 ◽  
Vol 340 (4) ◽  
pp. 766-793 ◽  
Author(s):  
Daniel W. Cranston ◽  
Douglas B. West


2017 ◽  
Vol 123 (2) ◽  
Author(s):  
Tingkai Zhao ◽  
Xianglin Ji ◽  
Wenbo Jin ◽  
Wenbo Yang ◽  
Xing Zhao ◽  
...  


2016 ◽  
Vol 109 (13) ◽  
pp. 133501 ◽  
Author(s):  
Tokihiro Ikeda ◽  
Takao M. Kojima ◽  
Yoshio Natsume ◽  
Jun Kimura ◽  
Tomoko Abe


10.37236/3252 ◽  
2013 ◽  
Vol 20 (2) ◽  
Author(s):  
Christopher Carl Heckman ◽  
Roi Krakovski

In 1995, Paul Erdös and András Gyárfás conjectured that for every graph of minimum degree at least 3, there exists a non-negative integer $m$ such that $G$ contains a simple cycle of length $2^m$. In this paper, we prove that the conjecture holds for 3-connected cubic planar graphs. The proof is long, computer-based in parts, and employs the Discharging Method in a novel way.



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