A degree sum condition for longest cycles in 3-connected graphs

2007 ◽  
Vol 54 (4) ◽  
pp. 277-283 ◽  
Author(s):  
Tomoki Yamashita
Keyword(s):  
Connected Graphs ◽  
Degree Sum ◽  
Longest Cycles ◽  
Degree Sum Condition

scholarly journals Degree sum conditions for the circumference of 4-connected graphs

2014 ◽  
Vol 333 ◽  
pp. 66-83
Author(s):  
Shuya Chiba ◽  
Masao Tsugaki ◽  
Tomoki Yamashita
Keyword(s):  
Connected Graphs ◽  
Degree Sum

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

Longest cycles in 3-connected graphs contain three contractible edges

1989 ◽  
Vol 13 (1) ◽  
pp. 17-21 ◽  
Author(s):  
Nathaniel Dean ◽  
Robert L. Hemminger ◽  
Katsuhiro Ota
Keyword(s):  
Connected Graphs ◽  
Longest Cycles

Smallest Sets of Longest Paths with Empty Intersection

1996 ◽  
Vol 5 (4) ◽  
pp. 429-436 ◽  
Author(s):  
Z. Skupień
Keyword(s):  
Connected Graph ◽  
Connected Graphs ◽  
Minimal Sets ◽  
Empty Intersection ◽  
Longest Cycles ◽  
Longest Paths

It is shown that, for every integer v < 7, there is a connected graph in which some v longest paths have empty intersection, but any v – 1 longest paths have a vertex in common. Moreover, connected graphs having seven or five minimal sets of longest paths (longest cycles) with empty intersection are presented. A 26-vertex 2-connected graph whose longest paths have empty intersection is exhibited.

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
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