Algebraically rigid simplicial complexes and graphs
نویسندگان
چکیده
منابع مشابه
Vertex Decomposable Simplicial Complexes Associated to Path Graphs
Introduction Vertex decomposability of a simplicial complex is a combinatorial topological concept which is related to the algebraic properties of the Stanley-Reisner ring of the simplicial complex. This notion was first defined by Provan and Billera in 1980 for k-decomposable pure complexes which is known as vertex decomposable when . Later Bjorner and Wachs extended this concept to non-pure ...
متن کامل9.2 Construction of Simplicial Complexes from Graphs
We can construct the neighborhood complex N(G), with vertices v1, ..., vn, from the graph G, in such a way that, for each vertex v of G, there is a simplex containing the vertex v along with its neighbouring vertices, corresponding to the directed edges v → w. To construct this, we can take each vertex in v1, ..., vn one by one, and construct the simplex along with it’s neighbors, each time. Th...
متن کاملEmbedding graphs into two-dimensional simplicial complexes
We consider the problem of deciding whether an input graph G admits a topological embedding into a two-dimensional simplicial complex C . This problem includes, among others, the embeddability problem of a graph on a surface and the topological crossing number of a graph, but is more general. The problem is NP-complete when C is part of the input, and we give a polynomial-time algorithm if the ...
متن کاملIncreasing spanning forests in graphs and simplicial complexes
Let G be a graph with vertex set {1, . . . , n}. A spanning forest F of G is increasing if the sequence of labels on any path starting at the minimum vertex of a tree of F forms an increasing sequence. Hallam and Sagan showed that the generating function ISF(G, t) for increasing spanning forests of G has all nonpositive integral roots. Furthermore they proved that, up to a change of sign, this ...
متن کاملSEQUENTIALLY Sr SIMPLICIAL COMPLEXES AND SEQUENTIALLY S2 GRAPHS
We introduce sequentially Sr modules over a commutative graded ring and sequentially Sr simplicial complexes. This generalizes two properties for modules and simplicial complexes: being sequentially Cohen-Macaulay, and satisfying Serre’s condition Sr . In analogy with the sequentially CohenMacaulay property, we show that a simplicial complex is sequentially Sr if and only if its pure i-skeleton...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2016
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2016.01.009