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- W1979898269 abstract "We study the ultimate independence ratio I(G) of a graph G , defined as the limit, as k →∞, of the sequence of independence ratios of the powers G k . We prove that I ( H )≤ I ( G ) if there is a homomorphism of G to H . This allows us to prove that 1/χ(G) ≤ I(G) ≤ 1/χ ƒ (G) , where χ ( G ) and χ ƒ (G) are the chromatic and the fractional chromatic numbers of G , respectively. From this result we derive a number of consequences: we construct graphs with I ( G ) strictly between 1/ χ ( G ) and i ( G ) (answering a question from an earlier paper). We estimate I ( G ) for some classes of graphs and, in some cases, we compute the exact value of I ( G ). In particular, we show that I(G) = 1 2 for all bipartite graphs G ." @default.
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- W1979898269 date "1995-05-01" @default.
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- W1979898269 title "On the ultimate independence ratio of a graph" @default.
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- W1979898269 doi "https://doi.org/10.1016/0195-6698(95)90030-6" @default.
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