On Characterization Of Spanning Forest Complexes

Abstract

In this thesis, we discuss the algebraic and combinatorial aspects of spanning forest complex ∆s(G) associated to simple disconnected graph G. We mainly emphasis on disjoint union of isomorphic copies graph G and provide special importance to tCn where tCn is the disjoint union of t cycles of length n and call this graph t-cycle graph. We give the characterization of s(tCn), all spanning forests, of tCn. We intend to provide the algebraic and combinatorial characterization of spanning forest complex ∆s(tCn) associated to tCn. In particular, we compute the formula for the f-vector of spanning forest complex of t-cycle graph. We also compute the h-vector and Hilbert series of Stanley Riesner ring k[∆s(tCn)]