Independence, irredundance, degrees and chromatic number in graphs
For a graph \(G\), let \(\beta\), IR, \(\delta\) and \(\Delta\) denote the independence number, the upper irredundance number, and the minimum and maximum degree of \(G\). It is proved that if \(\Delta\neq 0\), then \(\text{IR}\leq n/(1+\delta/\Delta)\) and \(\text{IR}-\beta\leq (\Delta- 2)n/(2\Delta)\). The second inequality proves a conjecture of Rautenbach.
scientific article; zbMATH DE number 1882155