The origin of the Li-rich K giants is still highly debated .
Here , we investigate the incidence of binarity among this family from a nine-year radial-velocity monitoring of a sample of 11 Li-rich K giants using the HERMES spectrograph attached to the 1.2m Mercator telescope .
A sample of 13 non-Li-rich giants ( 8 of them being surrounded by dust according to IRAS , WISE , and ISO data ) was monitored alongside .

When compared to the binary frequency in a reference sample of 190 K giants ( containing 17.4 % of definite spectroscopic binaries – SB – and 6.3 % of possible spectroscopic binaries – SB ?
) , the binary frequency appears normal among the Li-rich giants ( 2/11 definite binaries plus 2 possible binaries , or 18.2 % SB + 18.2 % SB ?
) , after taking account of the small sample size through the hypergeometric probability distribution .
Therefore , there appears to be no causal relationship between Li enrichment and binarity .
Moreover , there is no correlation between Li enrichment and the presence of circumstellar dust , and the only correlation that could be found between Li enrichment and rapid rotation is that the most Li-enriched K giants appear to be fast-rotating stars .
However , among the dusty K giants , the binary frequency is much higher ( 4/8 definite binaries plus 1 possible binary ) .
The remaining 3 dusty K giants suffer from a radial-velocity jitter , as is expected for the most luminous K giants , which these are .