Eulerian subgraphs in 3-edge-connected graphs and Hamiltonian line graphs

2003 ◽  
Vol 42 (4) ◽  
pp. 308-319 ◽  
Author(s):  
Zhi-Hong Chen ◽  
Hong-Jian Lai ◽  
Xiangwen Li ◽  
Deying Li ◽  
Jinzhong Mao
Keyword(s):  
Line Graphs ◽  
Connected Graphs ◽  
Hamiltonian Line Graphs ◽  
Eulerian Subgraphs

scholarly journals Lai's Conditions for Spanning and Dominating Closed Trails

10.37236/4511 ◽  
2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Wei-Guo Chen ◽  
Zhi-Hong Chen ◽  
Mei Lu
Keyword(s):  
Graph Theory ◽  
Real Number ◽  
Connected Graph ◽  
Finite Family ◽  
Discrete Mathematics ◽  
Line Graphs ◽  
Connected Graphs ◽  
Supereulerian Graphs ◽  
The Family ◽  
Hamiltonian Line Graphs

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].

scholarly journals Eulerian subgraphs and Hamilton-connected line graphs

2005 ◽  
Vol 145 (3) ◽  
pp. 422-428 ◽  
Author(s):  
Dengxin Li ◽  
Hong-Jian Lai ◽  
Mingquan Zhan
Keyword(s):  
Line Graphs ◽  
Eulerian Subgraphs ◽  
Hamilton Connected

Ons-Hamiltonian Line Graphs

2013 ◽  
Vol 74 (3) ◽  
pp. 344-358 ◽  
Author(s):  
Hong-Jian Lai ◽  
Yehong Shao
Keyword(s):  
Line Graphs ◽  
Hamiltonian Line Graphs

Onn-distant Hamiltonian line graphs

1977 ◽  
Vol 16 (3) ◽  
pp. 315-316
Author(s):  
Linda M. Lesniak
Keyword(s):  
Line Graphs ◽  
Hamiltonian Line Graphs

Hamiltonian line graphs

1981 ◽  
Vol 5 (3) ◽  
pp. 307-314 ◽  
Author(s):  
Richard A. Brualdi ◽  
Robert F. Shanny
Keyword(s):  
Line Graphs ◽  
Hamiltonian Line Graphs

scholarly journals On n-Hamiltonian line graphs

1977 ◽  
Vol 22 (3) ◽  
pp. 263-273 ◽  
Author(s):  
Linda Lesniak-Foster
Keyword(s):  
Line Graphs ◽  
Hamiltonian Line Graphs

scholarly journals Circumference of 3-connected claw-free graphs and large Eulerian subgraphs of 3-edge-connected graphs

2011 ◽  
Vol 101 (4) ◽  
pp. 214-236 ◽  
Author(s):  
Mark Bilinski ◽  
Bill Jackson ◽  
Jie Ma ◽  
Xingxing Yu
Keyword(s):  
Connected Graphs ◽  
Eulerian Subgraphs
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