Neighborhood Complexes of Some Exponential Graphs

[摘要] In this article, we consider the bipartite graphs $K_2 \times K_n$. We first show that the connectedness of the neighborhood complex $\mathcal{N}(K_{n+1}^{K_n}) =0$. Further, we show that Hom$(K_2 \times K_{n}, K_{m})$ is homotopic to $S^{m-2}$, if $2\leq

[学科分类] 离散数学和组合数学

[关键词] Hom Complexes;Exponential Graphs;Discrete Morse Theory