Toughness and the existence of fractional k-factors of graphs
نویسندگان
چکیده
منابع مشابه
Toughness of graphs and the existence of factors
The toughness of a graph G, denoted by t(G), is defined as the largest real number t such that the deletion of any s vertices from G results in a graph which is either connected or else has at most s/t components. Chvatal who introduced the concept of toughness in [2] conjectured that if G is a graph and k a positive integer such that k IV(G)1 IS even and t(G) 2 k then G has a k-factor. In [3] ...
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15 صفحه اولIsolated Toughness and Existence of [a, b]-factors in Graphs
For a graph G with vertex set V (G) and edge set E(G), let i(G) be the number of isolated vertices in G, the isolated toughness of G is defined as I(G) = min{|S|/i(G− S) | S ⊆ V (G), i(G− S) ≥ 2}, if G is not complete; and I(Kn) = n − 1. In this paper, we investigate the existence of [a, b]-factor in terms of this graph invariant. We proved that if G is a graph with δ(G) ≥ a and I(G) ≥ a, then ...
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In computer networks, toughness is an important parameter which is used to measure the vulnerability of the network. Zhou et al. [24] obtains a toughness condition for a graph to be fractional (k,m)–deleted and presents an example to show the sharpness of the toughness bound. In this paper we remark that the previous example does not work and inspired by this fact, we present a new toughness co...
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1 School of Mathematics and System Sciences, Shandong University, Jinan 250100, China 2 Department of Computer Science, Memorial University of Newfoundland, St. John’s, NL, Canada A1B 3X5 3 School of Computing, The University of Southern Mississippi, Hattiesburg, MS 39406, USA 4 Department of Mathematics, College of Arts and Sciences, The State University of West Georgia, Carrollton, GA 30118, USA
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2008
ISSN: 0012-365X
DOI: 10.1016/j.disc.2006.09.048