Uniform cyclic edge connectivity in cubic graphs

COMBINATORICA ◽  
1991 ◽  
Vol 11 (2) ◽  
pp. 81-96 ◽  
Author(s):  
R. E. L. Aldred ◽  
D. A. Holton ◽  
Bill Jackson
Keyword(s):  
Cubic Graphs ◽  
Edge Connectivity ◽  
Cyclic Edge Connectivity

An Algorithm for Cyclic Edge Connectivity of Cubic Graphs

2004 ◽  
pp. 236-247 ◽  
Author(s):  
Zdeněk Dvořák ◽  
Jan Kára ◽  
Daniel Král’ ◽  
Ondřej Pangrác
Keyword(s):  
Cubic Graphs ◽  
Edge Connectivity ◽  
Cyclic Edge Connectivity

scholarly journals Flows in Signed Graphs with Two Negative Edges

10.37236/4458 ◽  
2018 ◽  
Vol 25 (2) ◽  
Author(s):  
Edita Rollová ◽  
Michael Schubert ◽  
Eckhard Steffen
Keyword(s):  
Signed Graph ◽  
Cubic Graphs ◽  
Cubic Graph ◽  
Signed Graphs ◽  
Flow Number ◽  
Edge Connectivity ◽  
Cyclic Edge Connectivity

The presented paper studies the flow number $F(G,\sigma)$ of flow-admissible signed graphs $(G,\sigma)$ with two negative edges. We restrict our study to cubic graphs, because for each non-cubic signed graph $(G,\sigma)$ there is a set of cubic graphs obtained from $(G,\sigma)$ such that the flow number of $(G,\sigma)$ does not exceed the flow number of any of the cubic graphs. We prove that $F(G,\sigma) \leq 6$ if $(G,\sigma)$ contains a bridge, and $F(G,\sigma) \leq 7$ in general. We prove better bounds, if there is a cubic graph $(H,\sigma_H)$ obtained from $(G,\sigma)$ which satisfies some additional conditions. In particular, if $H$ is bipartite, then $F(G,\sigma) \leq 4$ and the bound is tight. If $H$ is $3$-edge-colorable or critical or if it has a sufficient cyclic edge-connectivity, then $F(G,\sigma) \leq 6$. Furthermore, if Tutte's $5$-Flow Conjecture is true, then $(G,\sigma)$ admits a nowhere-zero $6$-flow endowed with some strong properties.

scholarly journals Spectral Threshold for Extremal Cyclic Edge-Connectivity

2021 ◽  
Author(s):  
Sinan G. Aksoy ◽  
Mark Kempton ◽  
Stephen J. Young
Keyword(s):  
Edge Connectivity ◽  
Cyclic Edge Connectivity

scholarly journals Lower bound of cyclic edge connectivity for n-extendability of regular graphs

1993 ◽  
Vol 112 (1-3) ◽  
pp. 139-150 ◽  
Author(s):  
Dingjun Lou ◽  
D.A. Holton
Keyword(s):  
Lower Bound ◽  
Regular Graphs ◽  
Edge Connectivity ◽  
Cyclic Edge Connectivity

The Cyclic Edge Connectivity and Anti-Kekulé Number of the (5,6,7)-Fullerene

2017 ◽  
Vol 40 (1) ◽  
pp. 144-149
Author(s):  
Shengzhang Ren ◽  
Tingzeng Wu ◽  
Heping Zhang
Keyword(s):  
Edge Connectivity ◽  
Cyclic Edge Connectivity

scholarly journals On cyclic edge-connectivity of fullerenes

2008 ◽  
Vol 156 (10) ◽  
pp. 1661-1669 ◽  
Author(s):  
Klavdija Kutnar ◽  
Dragan Marušič
Keyword(s):  
Edge Connectivity ◽  
Cyclic Edge Connectivity
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