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1994, Journal of applied probability
Here we give a necessary and sufficient condition for the convergence to a random max infinitely divisible law from that of a random maximum. We then discuss random max-stable laws, their domain of max-attraction and the associated extremal processes.
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A correction on the signed bad numberA signed bad function of [Formula: see text] is a function [Formula: see text] such that [Formula: see text] for every [Formula: see text] where [Formula: see text] is the closed neighborhood of [Formula: see text]. The signed bad number is [Formula: see text]. Ghameshlou et al. [A. N. Ghameshlou, A. Khodkar and S. M. Sheikholeslami, The signed bad numbers in graphs, Discrete Math. Algorithms Appl. 1 (2011) 33–41] proved that for any bipartite graph of order [Formula: see text], [Formula: see text]. But their proof has a gap and the bound is not correct in general. In this note, we modify their proof and show that for any bipartite graph of order [Formula: see text], [Formula: see text], and also we characterize the bipartite graphs attaining this bound.
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