Independence, odd girth, and average degree

  title={Independence, odd girth, and average degree},
  author={Christian L{\"o}wenstein and Anders Sune Pedersen and Dieter Rautenbach and Friedrich Regen},
  journal={Journal of Graph Theory},
We prove several best-possible lower bounds in terms of the order and the average degree for the independence number of graphs which are connected and/or satisfy some odd girth condition. Our main result is the extension of a lower bound for the independence number of triangle-free graphs of maximum degree at most 3 due to Heckman and Thomas [A New Proof of the Independence Ratio of Triangle-Free Cubic Graphs, Discrete Math. 233 (2001), 233-237] to arbitrary triangle-free graphs. For connected… CONTINUE READING