On extremal k-outconnected graphs

Let G be a minimally k-connected graph with n nodes and m edges. Mader proved that if n 3k - 2 then m k(n - k), and for n 3k - 1 an equality is possible if, and only if, G is the complete bipartite graph Kk,n-k. Cai proved that if n 3k - 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. Key-words: minimally k-outconnected graphs, extremal graphs

• Type: Journal
• Year: 2008
• Where: DM
• Authors: Zeev Nutov
• Keywords: Complete Bipartite Graph, DM 2008, K-connected Graph, K-outconnected Graphs