scholarly journals Degree sum condition for fractional ID-$k$-factor-critical graphs

2017 ◽  
Vol 18 (2) ◽  
pp. 751 ◽  
Author(s):  
Wei Gao ◽  
Weifan Wang
Keyword(s):  
Critical Graphs ◽  
Degree Sum ◽  
K Factor ◽  
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

Remarks on Fractional ID-k-factor-critical Graphs

2019 ◽  
Vol 35 (2) ◽  
pp. 458-464 ◽  
Author(s):  
Si-zhong Zhou ◽  
Lan Xu ◽  
Zu-run Xu
Keyword(s):  
Critical Graphs ◽  
K Factor

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

A conjecture on k-factor-critical and 3-γ-critical graphs

2010 ◽  
Vol 53 (5) ◽  
pp. 1385-1391 ◽  
Author(s):  
Tao Wang ◽  
QingLin Yu
Keyword(s):  
Critical Graphs ◽  
K Factor
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