A note on single-linkage equivalence

A note on single-linkage equivalence

We introduce the concept of single-linkage equivalence of edge-weighted graphs, we apply it to characterise maximal spanning trees and “ultrasimilarities”, and we discuss how it relates to the popular single-linkage clustering algorithm.

A note on equivalence in ranking investments

A note on tall cardinals and level by level equivalence

Starting from a model V “ZFC + GCH + κ is supercompact + No cardinal is supercompact up to a measurable cardinal”, we force and construct a model V P such that V P “ZFC + κ is supercompact + No cardinal is supercompact up to a measurable cardinal + δ is measurable iff δ is tall” in which level by level equivalence between strong compactness and supercompactness holds. This extends and generaliz...

A Note on Aumann’s Core Equivalence Theorem without Monotonicity∗

In an exchange economy with a continuum of traders, we establish the equivalence theorem on the core and the set of competitive allocations without assuming monotonicity of traders’ preferences. Under weak assumptions we provide two alternative core equivalence theorems. The first one is for irreducible economies under Debreu’s assumption on quasi-equilibria. The second one is an extension of A...

A Note on Maxflow-Mincut and Homomorphic Equivalence in Matroids

Graph homomorphisms are used to study good characterizations for coloring problems (Trans. Amer. Math. Soc. 384 (1996), 1281–1297; Discrete Math. 22 (1978), 287–300). Particularly, the following concept arises in this context: A pair of graphs (A, B) is called a homomorphism duality if for any graph G either there exists a homomorphism σ : A→ G or there exists a homomorphism τ : G → B but not b...