TY - JOUR
T1 - Decreasing the diameter of bounded degree graphs
AU - Alon, Noga
AU - Gyárfás, András
AU - Ruszinkó, Miklós
PY - 2000/11
Y1 - 2000/11
N2 - Let fd(G) denote the minimum number of edges that have to be added to a graph G to transform it into a graph of diameter at most d. We prove that for any graph G with maximum degree D and n > n0 (D) vertices, f2(G) = n - D - 1 and f3(G) ≥ n - O(D3). For d ≥ 4, fd(G) depends strongly on the actual structure of G, not only on the maximum degree of G. We prove that the maximum of fd (G) over all connected graphs on n vertices is n/[d/2] - O(1). As a byproduct, we show that for the n-cycle Cn, fd(Cn) = n/ (2[d/2] - 1) - O(1) for every d and n, improving earlier estimates of Chung and Garey in certain ranges.
AB - Let fd(G) denote the minimum number of edges that have to be added to a graph G to transform it into a graph of diameter at most d. We prove that for any graph G with maximum degree D and n > n0 (D) vertices, f2(G) = n - D - 1 and f3(G) ≥ n - O(D3). For d ≥ 4, fd(G) depends strongly on the actual structure of G, not only on the maximum degree of G. We prove that the maximum of fd (G) over all connected graphs on n vertices is n/[d/2] - O(1). As a byproduct, we show that for the n-cycle Cn, fd(Cn) = n/ (2[d/2] - 1) - O(1) for every d and n, improving earlier estimates of Chung and Garey in certain ranges.
KW - Diameter of graphs
KW - Graphs
KW - Maximum degree
UR - http://www.scopus.com/inward/record.url?scp=0042689506&partnerID=8YFLogxK
U2 - 10.1002/1097-0118(200011)35:3<161::AID-JGT1>3.0.CO;2-Y
DO - 10.1002/1097-0118(200011)35:3<161::AID-JGT1>3.0.CO;2-Y
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AN - SCOPUS:0042689506
SN - 0364-9024
VL - 35
SP - 161
EP - 172
JO - Journal of Graph Theory
JF - Journal of Graph Theory
IS - 3
ER -