scholarly journals Longest cycles in 4-connected graphs

2017 ◽  
Vol 340 (12) ◽  
pp. 2955-2966 ◽  
Author(s):  
Junqing Cai ◽  
Hao Li ◽  
Qiang Sun
Keyword(s):  
Connected Graphs ◽  
Longest Cycles

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.

Longest Cycles in 2-Connected Graphs with Prescribed Maximum Degree

1980 ◽  
Vol 32 (6) ◽  
pp. 1325-1332 ◽  
Author(s):  
J. A. Bondy ◽  
R. C. Entringer
Keyword(s):  
Connected Graph ◽  
Maximum Degree ◽  
Minimum Degree ◽  
Simple Graph ◽  
General Context ◽  
Connected Graphs ◽  
Longest Cycles ◽  
Image Position ◽  
The Relationship

The relationship between the lengths of cycles in a graph and the degrees of its vertices was first studied in a general context by G. A. Dirac. In [5], he proved that every 2-connected simple graph on n vertices with minimum degree d contains a cycle of length at least min{2d, n};. Dirac's theorem was subsequently strengthened in various directions in [7], [6], [13], [12], [2], [1], [11], [8], [14], [15] and [16].Our aim here is to investigate another aspect of this relationship, namely how the lengths of the cycles in a 2-connected graph depend on the maximum degree. Let us denote by ƒ(n, d) the largest integer k such that every 2-connected simple graph on n vertices with maximum degree d contains a cycle of length at least k. We prove in Section 2 that, for d ≧ 3 and n ≧ d + 2,

scholarly journals Intersections of Longest Cycles in k-Connected Graphs

1998 ◽  
Vol 72 (1) ◽  
pp. 143-149 ◽  
Author(s):  
Guantao Chen ◽  
Ralph J Faudree ◽  
Ronald J Gould
Keyword(s):  
Connected Graphs ◽  
Longest Cycles

scholarly journals Longest cycles in 3-connected graphs

1997 ◽  
Vol 170 (1-3) ◽  
pp. 195-201 ◽  
Author(s):  
B. Wei
Keyword(s):  
Connected Graphs ◽  
Longest Cycles

Removable Edges and Chords of Longest Cycles in 3-Connected Graphs

2013 ◽  
Vol 30 (3) ◽  
pp. 743-753 ◽  
Author(s):  
Jichang Wu ◽  
Hajo Broersma ◽  
Haiyan Kang
Keyword(s):  
Connected Graphs ◽  
Longest Cycles

scholarly journals Longest cycles in k-connected graphs with given independence number

2011 ◽  
Vol 101 (6) ◽  
pp. 480-485 ◽  
Author(s):  
Suil O ◽  
Douglas B. West ◽  
Hehui Wu
Keyword(s):  
Independence Number ◽  
Connected Graphs ◽  
Longest Cycles

On the Longest Cycles in a Class of 3-Connected Graphs

1989 ◽  
Vol 576 (1 Graph Theory) ◽  
pp. 107-117
Author(s):  
CHUANPING CHEN ◽  
YONGJIN ZHU
Keyword(s):  
Connected Graphs ◽  
Longest Cycles
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