[PDF][PDF] Maximal local edge-connectivity of diamond-free graphs.
A Holtkamp - Australas. J Comb., 2011 - Citeseer
A Holtkamp
Australas. J Comb., 2011•CiteseerThe edge-connectivity of a graph G can be defined as λ (G)= min {λG (u, v)| u, v∈ V (G)},
where λG (u, v) is the local edge-connectivity of two vertices u and v in G. We call a graph G
maximally edgeconnected when λ (G)= δ (G) and maximally local edge-connected when λG
(u, v)= min {d (u), d (v)} for all pairs u and v of distinct vertices in G. In 2000, Fricke,
Oellermann and Swart (unpublished manuscript) proved that a bipartite graph G of order n
(G) is maximally local edgeconnected when n (G)≤ 4δ (G)− 1. As an extension of this result …
where λG (u, v) is the local edge-connectivity of two vertices u and v in G. We call a graph G
maximally edgeconnected when λ (G)= δ (G) and maximally local edge-connected when λG
(u, v)= min {d (u), d (v)} for all pairs u and v of distinct vertices in G. In 2000, Fricke,
Oellermann and Swart (unpublished manuscript) proved that a bipartite graph G of order n
(G) is maximally local edgeconnected when n (G)≤ 4δ (G)− 1. As an extension of this result …
Abstract
The edge-connectivity of a graph G can be defined as λ (G)= min {λG (u, v)| u, v∈ V (G)}, where λG (u, v) is the local edge-connectivity of two vertices u and v in G. We call a graph G maximally edgeconnected when λ (G)= δ (G) and maximally local edge-connected when λG (u, v)= min {d (u), d (v)} for all pairs u and v of distinct vertices in G.
In 2000, Fricke, Oellermann and Swart (unpublished manuscript) proved that a bipartite graph G of order n (G) is maximally local edgeconnected when n (G)≤ 4δ (G)− 1. As an extension of this result, we will show in this work that it is sufficient for G to be diamond-free with n (G)≤ 4δ (G)− 1 to guarantee the maximally local edge-connectivity.
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