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Title: On the higher-order edge toughness of a graph
Authors: Chen, C.C. 
Koh, K.M. 
Peng, Y.H.
Issue Date: 22-Feb-1993
Citation: Chen, C.C.,Koh, K.M.,Peng, Y.H. (1993-02-22). On the higher-order edge toughness of a graph. Discrete Mathematics 111 (1-3) : 113-123. ScholarBank@NUS Repository.
Abstract: For an integer c, 1≤c≤{curly logical or}V(G){curly logical or}-1, we define the cth-order edge toughness of a graph G as tc(G)=min |X| ω(G-X)-cX⊆E(G) & ω(G-X)>c The objective of this paper is to study this generalized concept of edge toughness. Besides giving the of the cth-order edge toughness τc(G) of a graph G, we prove that 'τc(G)≥k if and only if G has k edge-disjoint spanning forests with exactly c components'. We also study the 'balancity' of a graph G of order p and size q, which is defined as the smallest positive integer c such that τc(G) = p/(p-c). © 1993.
Source Title: Discrete Mathematics
ISSN: 0012365X
Appears in Collections:Staff Publications

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