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On the higher-order edge toughness of a graph

✍ Scribed by C.C. Chen; K.M. Koh; Y.H. Peng

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
571 KB
Volume
111
Category
Article
ISSN
0012-365X

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✦ Synopsis

Chen CC., K.M. Koh and Y.H. Peng, On the higher-order edge toughness of a graph, Discrete Mathematics 111 (1993) 113-123.

For an integer c, 1 <c < 1 V(G) I-1, we define the cth-order edye toughness of a graph G as

The objective of this paper is to study this generalized concept of edge toughness. Besides giving the bounds and relationships of the cth-order edge toughness T,(G) of a graph G, we prove that 's,(G) 2 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 r,(G)=q/( p-c).

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Let G be a graph and let t Υ† 0 be a real number. Then, We discuss how the toughness of (spanning) subgraphs of G and related graphs depends on (G), we give some sufficient degree conditions implying that (G) Υ† t, and we study which subdivisions of 2-connected graphs have minimally 2-tough squares.