On the independence ratio of a graph
Michael O. Albertson, Joan P. Hutchinson · Journal of Graph Theory · 1978
Abstract This paper presents some recent results on lower bounds for independence ratios of graphs of positive genus and shows that in a limiting sense these graphs have the same independence ratios as do planar graphs. This last result is obtained by an application of Menger's Theorem to show that every triangulation of a surface of positive genus has a short cycle which does not separate the graph and is non‐contractible on that surface.