Toughness and [a,b]-factors with inclusion/exclusion properties |
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| Authors: | WU ZeFang LIU GuiZhen & YU QingLin Center for Combinatorics LPMC-TJKLC Nankai University Tianjin China School of Mathematics Sh ong University Jinan |
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| Institution: | WU ZeFang1,LIU GuiZhen2 & YU QingLin2,3,1Center for Combinatorics,LPMC-TJKLC,Nankai University,Tianjin 300071,China,2School of Mathematics,Shandong University,Jinan 250100,3Department of Mathematics and Statistics,Thompson Rivers University,Kamloops V2C 5N3,Canada |
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| Abstract: | In this paper, we investigate the existence of a,b]-factors with inclusion/exclusion properties under the toughness condition. We prove that if an incomplete graph G satisfies t(G) (a-1) + ab and a,b are two integers with b > a > 1, then for any two given edges e1 and e2, there exist an a,b]-factor including e1,e2; and an a,b]-factor including e1 and excluding e2; as well as an a,b]-factor excluding e1,e2 unless e1 and e2 have a common end in the case of a = 2. For complete graphs, we obtain a similar r... |
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| Keywords: | [a b]-factor inclusion/exclusion property toughness |
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