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Independence Number, Connectivity and All Fractional (a, b, k)-Critical Graphs

By Yuan Yuan and Hao Rong-Xia

Abstract

Let G be a graph and a, b and k be nonnegative integers with 1 ≤ a ≤ b. A graph G is defined as all fractional (a, b, k)-critical if after deleting any k vertices of G, the remaining graph has all fractional [a, b]-factors. In this paper, we prove that if , then G is all fractional (a, b, k) -critical. If k = 0, we improve the result given in [Filomat 29 (2015) 757-761]. Moreover, we show that this result is best possible in some sense

Topics: independence number, connectivity, fractional [a, b]-factor, frac- tional (a, b, k)-critical graph, all fractional (a, b, k)-critical graph, 05C70, 05C72, Mathematics, QA1-939
Publisher: Sciendo
Year: 2019
DOI identifier: 10.7151/dmgt.2075
OAI identifier: oai:doaj.org/article:c109a3b15fc64097b918557ad5bcbd1a
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