Abstract#R##N##R##N#A cut-set in an undirected multigraph G is a subset of edges whose removal makes the graph disconnected. Let mi(G) denote the number of all cut-sets, each of which consists of i edges. In this paper, for any multigraph G with n nodes and e (⩾3n/2) edges, we show that mi(G) with α ⩽ i ⩽ 2(α - γ) - 3, where α = ⌊2e/n⌋ and γ = ⌊2e/n(n - 1)⌋, is greater than or equal to ()((α + 1)n - 2e) + ()(2e -αn). A necessary and sufficient condition for a multigraph G with given n and e to minimize mi(G) for an i with i ⩽ 2(α - γ) - 3 is presented. We also show that there exists a graph such that the lower bound is tight for all i in the range [α, 2(α - γ) - 3]. © 1994 by John Wiley & Sons, Inc.
['Hideaki Harada', 'Zheng Sun', 'Hiroshi Nagamochi']
An exact lower bound on the number of cut‐sets in multigraphs