TY - JOUR

T1 - On extremal k-outconnected graphs

AU - Nutov, Zeev

N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2008/6/28

Y1 - 2008/6/28

N2 - Let G be a minimally k-connected graph with n nodes and m edges. Mader proved that if n ≥ 3 k - 2 then m ≤ k (n - k), and for n ≥ 3 k - 1 an equality is possible if, and only if, G is the complete bipartite graph Kk, n - k. Cai proved that if n ≤ 3 k - 2 then m ≤ ⌊ (n + k)2 / 8 ⌋, and listed the cases when this bound is tight. In this paper we prove a more general theorem, which implies similar results for minimally k-outconnected graphs; a graph is called k-outconnected from r if it contains k internally disjoint paths from r to every other node.

AB - Let G be a minimally k-connected graph with n nodes and m edges. Mader proved that if n ≥ 3 k - 2 then m ≤ k (n - k), and for n ≥ 3 k - 1 an equality is possible if, and only if, G is the complete bipartite graph Kk, n - k. Cai proved that if n ≤ 3 k - 2 then m ≤ ⌊ (n + k)2 / 8 ⌋, and listed the cases when this bound is tight. In this paper we prove a more general theorem, which implies similar results for minimally k-outconnected graphs; a graph is called k-outconnected from r if it contains k internally disjoint paths from r to every other node.

KW - Extremal graphs

KW - Minimally k-outconnected graphs

UR - http://www.scopus.com/inward/record.url?scp=41549123553&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2007.06.011

DO - 10.1016/j.disc.2007.06.011

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AN - SCOPUS:41549123553

SN - 0012-365X

VL - 308

SP - 2533

EP - 2543

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 12

ER -