Linear Residuals and Gallai-Simplicial Complexes

2016/12/12 by Anwar, Imran, Kosar, Zunaira, Nazir, Shaheen +1
#13P10 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1612.03544

Abstract

In this paper, we give a new algebraic criterion for the \em shellability of (non-pure) simplicial complex Δ over [n], shellable in the sense of Björner and Wachs \citeBW. We show that the spanning simplicial complex of doubly uni-cyclic graph is non-pure shellable. Moreover, we introduce the concept of Gallai-simplicial complex Δ_Γ(G) of a finite simple graph G. We applied the obtained criterion to discuss the shellability of Gallai simplicial complexes associated to various classes of graphs..

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