A finiteness theorem for maximal independent sets

Denote bymi(G) the number of maximal independent sets ofG. This paper studies the setS(k) of all graphsG withmi(G) = k and without isolated vertices (exceptG K ₁) or duplicated vertices. We determineS(1), S(2), andS(3) and prove that |V(G)| 2 ^k–1 +k – 2 for anyG inS(k) andk 2; consequently,S(k) is finite for anyk. Supported in part by the National Science Council under grant NSC 83-0208-M009-050     

Existence results for superlinear semipositone 's

We consider the existence of positive solutions to the BVP

where . Our results extend some of the existing literature on superlinear semipositone problems and singular BVPs. Our proofs are quite simple and are based on fixed point theorems in a cone.