Cluster-growth model for branched polymers that are "chemically linear"

We propose a new cluster-growth model for branched polymers which are highly unusual in that they are "chemically linear." The cluster grows by adding a constant number of sites in each successive "chemical shell." We find that these chemically linear clusters (where branches and loops are allowed) are in the same universality class as geometrically linear chains (where loops and branches are not allowed). We argue that this result is general in that for any chemically linear cluster, loops and branches can be neglected.