Long cycles passing through a specified edge in a 3‐connected graph
H Enomoto, K Hirohata, K Ota - Journal of Graph Theory, 1997 - Wiley Online Library
We prove the following theorem: For a connected noncomplete graph G, let τ (G):= min {dG
(u)+ dG (v)| dG (u, v)= 2}. Suppose G is a 3‐connected noncomplete graph. Then through
each edge of G there passes a cycle of length≥ min {| V (G)|, τ (G)− 1}.© 1997 John Wiley &
Sons, Inc.
(u)+ dG (v)| dG (u, v)= 2}. Suppose G is a 3‐connected noncomplete graph. Then through
each edge of G there passes a cycle of length≥ min {| V (G)|, τ (G)− 1}.© 1997 John Wiley &
Sons, Inc.
Long cycles passing through a specified edge in 3-connected graphs
Z Sun, F Tian, B Wei - Graphs and Combinatorics, 2001 - Springer
In this paper we prove that if G is a 3-connected noncomplete graph of order n satisfying that
the degree sum of any two vertices with distance 2 is not less than m, then either there exists
a cycle containing e of length at least min {n, m} for any edge e of G, or or where l= 2 (n−
3)/(m− 4). The result improves a theorem in [3] and a theorem in [4], respectively.
the degree sum of any two vertices with distance 2 is not less than m, then either there exists
a cycle containing e of length at least min {n, m} for any edge e of G, or or where l= 2 (n−
3)/(m− 4). The result improves a theorem in [3] and a theorem in [4], respectively.
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