supereulerian graphs
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Author(s):  
Jia Wei ◽  
Zhifu You ◽  
Sulin Song ◽  
Hong-Jian Lai
Keyword(s):  


2021 ◽  
Vol 344 (3) ◽  
pp. 112239
Author(s):  
Lan Lei ◽  
Wei Xiong ◽  
Yikang Xie ◽  
Mingquan Zhan ◽  
Hong-Jian Lai


2020 ◽  
Vol 37 (1) ◽  
pp. 55-64
Author(s):  
Mansour J. Algefari ◽  
Hong-Jian Lai


2018 ◽  
Vol 341 (6) ◽  
pp. 1696-1707 ◽  
Author(s):  
Roman Čada ◽  
Kenta Ozeki ◽  
Liming Xiong ◽  
Kiyoshi Yoshimoto


2017 ◽  
Vol 340 (12) ◽  
pp. 2792-2797 ◽  
Author(s):  
Shipeng Wang ◽  
Liming Xiong


2016 ◽  
Vol 32 (6) ◽  
pp. 2267-2273
Author(s):  
Zhi-Hong Chen
Keyword(s):  


2016 ◽  
Vol 202 ◽  
pp. 111-130 ◽  
Author(s):  
Xiaoling Ma ◽  
Hong-Jian Lai ◽  
Wei Xiong ◽  
Baoyindureng Wu ◽  
Xinhui An
Keyword(s):  


2016 ◽  
Vol 200 ◽  
pp. 79-94 ◽  
Author(s):  
Ping Li ◽  
Hao Li ◽  
Ye Chen ◽  
Herbert Fleischner ◽  
Hong-Jian Lai


10.37236/4511 ◽  
2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Wei-Guo Chen ◽  
Zhi-Hong Chen ◽  
Mei Lu

A graph is supereulerian if it has a spanning closed trail. For an integer $r$, let ${\cal Q}_0(r)$ be  the family of 3-edge-connected nonsupereulerian graphs of order at most $r$. For a graph $G$, define $\delta_L(G)=\min\{\max\{d(u), d(v) \}| \  \mbox{ for any $uv\in E(G)$} \}$. For a given integer $p\ge 2$ and a given real number $\epsilon$,  a graph $G$ of order $n$ is said to satisfy a Lai's condition if $\delta_L(G)\ge \frac{n}{p}-\epsilon$.  In this paper, we show that  if $G$ is  a  3-edge-connected graph of order $n$ with $\delta_L(G)\ge \frac{n}{p}-\epsilon$, then there is an integer $N(p, \epsilon)$ such that when $n> N(p,\epsilon)$, $G$ is supereulerian if and only if $G$ is not  a graph obtained from a  graph $G_p$ in the finite family ${\cal Q}_0(3p-5)$ by replacing some vertices in $G_p$ with nontrivial graphs. Results on the best possible Lai's  conditions for Hamiltonian line graphs of 3-edge-connected graphs or 3-edge-connected supereulerian graphs are given,  which are improvements of the results in [J. Graph Theory 42(2003) 308-319] and in [Discrete Mathematics, 310(2010) 2455-2459].



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