The scattering number and isolated scattering number of a graph have been introduced in relation to Hamiltonian properties and network vulnerability, and the isolated scattering number plays an important role in characterizing graphs with a fractional 1-factor. Here we investigate the computational complexity of one variant, namely, the weighted isolated scattering number. We give a polynomial time algorithm to compute this parameter of interval graphs, an important subclass of perfect graphs.

The COVID-19 pandemic has created enormous challenges for organizations and employees. Due to the effectiveness of idiosyncratic deals in management practices, more and more organizations use this human resource management tool to address the challenges posed by the COVID-19 pandemic. However, whether there are potential risks or negative effects of i-deals in the COVID-19 pandemic environment is not very clear. Drawing upon social cognitive theory, we proposed that i-deals may foment focal employees’ unethical behavior by triggering their hubristic pride, and (...) such process may be moderated by their trait of grandiose narcissism. We conducted a survey during the COVID-19 outbreak and tested our hypotheses with 492 samples from Shandong Province, China. Consistent with predictions, we found a positive relationship between i-deals and hubristic pride, which, in turn, increased their unethical behavior. And the relationship between i-deals and unethical behavior was mediated by hubristic pride. Furthermore, grandiose narcissism strengthened the positive relationship between i-deals and hubristic pride, as well as the indirect effect of i-deals on unethical behavior via hubristic pride. Our findings contributed to the literature on i-deals and provided guidance for organizations to address the challenges posed by the COVID-19 pandemic. (shrink)