Abstract
Wei discovered that the independence number of a graph G is at least Σ v (1 + d( v)) −1. It is proved here that if G is a connected triangle-free graph on n ≥ 3 vertices and if G is neither an odd cycle nor an odd path, then the bound above can be increased by n Δ(Δ + 1) , where Δ is the maximum degree. This new bound is sharp for even cycles and for three other graphs. These results relate nicely to some algorithms for finding large independent sets. They also have a natural matrix theory interpretation. A survey of other known lower bounds on the independence number is presented.
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