The problems Contractibility and Induced Minor are to test whether a graph G contains a graph H as a contraction or as an induced minor, respectively. We show that these two problems can be solved in |VG|H |) time if G is a chordal input graph and H is a split graph or a tree. In contrast, we show that containment relations extending Subgraph Isomorphism can be solved in linear time if G is a c...

In this paper we study the topology of the strata, indexed by number partitions λ, in the natural stratification of the space of monic hyperbolic polynomials of degree n. We prove stabilization theorems for removing an independent block or an independent relation in λ. We also prove contractibility of the one-point compactifications of the strata indexed by a large class of number partitions, i...

We consider a class of holographic tensor networks that are efficiently contractible variational ansatze, manifestly (approximate) quantum error correction codes, and can support power-law correlation functions. In the case when network consists single type also acts as an erasure code, we show it cannot be both locally sustain Motivated by this no-go theorem, desirability local contractibility...

We study the computational complexity of graph planarization via edge contraction. The problem Contract asks whether there exists a set S of at most k edges that when contracted produces a planar graph. We work with a more general problem called P -RestrictedContract in which S, in addition, is required to satisfy a fixed MSOL formula P (S,G). We give an FPT algorithm in time O(nf(k)) which sol...

It is shown that the group of automorphisms of a nonatomic finite measure space is contractible. 1. In [l] S. Harada showed that the automorphism group of the unit interval with Lebesgue measure is simple and arcwise connected. Our purpose here is to give a simple proof that the automorphism group G of a nonatomic measure space (ß, (B, m) with rez(ß)< oo is contractible. The contraction map wil...

One salient characteristic of poorly developed capital markets is the excessive weight they give to the availability of hard assets in the allocation of financial funds. Where external finance contractibility is poor, higher proportions of assets that more easily remain with investors if the relationship breaks down are used in order to sustain external finance. Consistent with this view, I sho...