Mar 21, 2020 · Abstract:Tutte proved that every 4-connected planar graph contains a Hamilton cycle, but there are 3-connected n-vertex planar graphs whose ...
Feb 28, 2011 · The first result states that every 4-connected graph G with minimum degree δ and connectivity κ either contains a cycle of length at least 4 ...
Every 4-connected graph $G$ with minimum degree $\delta$ and connectivity $\kappa$ either contains a cycle of length at least $4\delta-\kappa-4$ or every ...
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Let G be a 4-connected planar graph on n vertices. Previous results show that G contains a cycle of length k for each k∈{n,n−1,n−2,n−3} with k≥3.
A 3-connected cubic graph is cyclically 4-connected if it has at least 𝑛 ≥ 8 vertices and when removal of a set of three edges results in a disconnected ...
May 29, 2018 · It is very easy to find a Hamiltonian cycle in this graph. First find a cycle in the inner 6x6 grid graph. Then replace four of the outer edges ...
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Tutte proved that every 4-connected planar graph contains a Hamilton cycle, but there are 3-connected n-vertex planar graphs whose longest cycles have ...
[PDF] Large cycles in 4-connected graphs | Semantic Scholar
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In this paper we supply bounds for the length of a longest cycle C in G in terms of the structure of G-V(C).
May 31, 2024 · The famous Tutte theorem on the Hamilton cycle states that every 4-connected planar graph contains a Hamilton cycle.
If every 3-separator S of G is trivial, we call the 3-connected planar graph. G essentially 4-connected. In the present paper, we are interested in lower bounds.