scholarly journals A Degree Sum Condition for Hamiltonian Graphs

2021 ◽  
Vol 1 ◽  
pp. 85-88
Keyword(s):  
Hamiltonian Graphs ◽  
Degree Sum ◽  
Degree Sum Condition

On a Sharp Degree Sum Condition for Disjoint Chorded Cycles in Graphs

2010 ◽  
Vol 26 (2) ◽  
pp. 173-186 ◽  
Author(s):  
Shuya Chiba ◽  
Shinya Fujita ◽  
Yunshu Gao ◽  
Guojun Li
Keyword(s):  
Degree Sum ◽  
Chorded Cycles ◽  
Degree Sum Condition

scholarly journals Vertex Degree Sums for Matchings in 3-Uniform Hypergraphs

10.37236/8627 ◽  
2019 ◽  
Vol 26 (4) ◽  
Author(s):  
Yi Zhang ◽  
Yi Zhao ◽  
Mei Lu
Keyword(s):  
Vertex Degree ◽  
Uniform Hypergraph ◽  
Degree Sum ◽  
Uniform Hypergraphs ◽  
Positive Integers ◽  
Degree Sum Condition

Let $n, s$ be positive integers such that $n$ is sufficiently large and $s\le n/3$. Suppose $H$ is a 3-uniform hypergraph of order $n$ without isolated vertices. If $\deg(u)+\deg(v) > 2(s-1)(n-1)$ for any two vertices $u$ and $v$ that are contained in some edge of $H$, then $H$ contains a matching of size $s$. This degree sum condition is best possible and confirms a conjecture of the authors [Electron. J. Combin. 25 (3), 2018], who proved the case when $s= n/3$.

scholarly journals Degree sum condition for the existence of spanning k-trees in star-free graphs

2019 ◽  
Author(s):  
Michitaka Furuya ◽  
Shun-ichi Maezawa ◽  
Ryota Matsubara ◽  
Haruhide Matsuda ◽  
Shoichi Tsuchiya ◽  
...  
Keyword(s):  
Degree Sum ◽  
Degree Sum Condition

scholarly journals A degree sum condition for graphs to be covered by two cycles

2010 ◽  
Vol 310 (13-14) ◽  
pp. 1864-1874
Author(s):  
Shuya Chiba ◽  
Masao Tsugaki
Keyword(s):  
Degree Sum ◽  
Degree Sum Condition

scholarly journals A degree sum condition for long cycles passing through a linear forest

2008 ◽  
Vol 308 (12) ◽  
pp. 2382-2388
Author(s):  
Jun Fujisawa ◽  
Tomoki Yamashita
Keyword(s):  
Degree Sum ◽  
Linear Forest ◽  
Long Cycles ◽  
Degree Sum Condition

scholarly journals A Degree Sum Condition on the Order, the Connectivity and the Independence Number for Hamiltonicity

10.37236/5480 ◽  
2019 ◽  
Vol 26 (4) ◽  
Author(s):  
Shuya Chiba ◽  
Michitaka Furuya ◽  
Kenta Ozeki ◽  
Masao Tsugaki ◽  
Tomoki Yamashita
Keyword(s):  
Connected Graph ◽  
Minimum Degree ◽  
Independence Number ◽  
Hamilton Cycle ◽  
Degree Sum ◽  
The Third ◽  
Degree Sum Condition

In [Graphs Combin. 24 (2008) 469–483], the third author and the fifth author conjectured that if $G$ is a $k$-connected graph such that $\sigma_{k+1}(G) \ge |V(G)|+\kappa(G)+(k-2)(\alpha(G)-1)$, then $G$ contains a Hamilton cycle, where $\sigma_{k+1}(G)$, $\kappa(G)$ and $\alpha(G)$ are the minimum degree sum of $k+1$ independent vertices, the connectivity and the independence number of $G$, respectively. In this paper, we settle this conjecture. The degree sum condition is best possible.  

Sign in / Sign up

Export Citation Format

Share Document