52,691 research outputs found
A closure concept in factor-critical graphs
AbstractA graph G is called n-factor-critical if the removal of every set of n vertices results in a~graph with a~1-factor. We prove the following theorem: Let G be a~graph and let x be a~locally n-connected vertex. Let {u,v} be a~pair of vertices in V(G)−{x} such that uv∉E(G), x∈NG(u)∩NG(v), and NG(x)⊂NG(u)∪NG(v)∪{u,v}. Then G is n-factor-critical if and only if G+uv is n-factor-critical
On stability of the Hamiltonian index under contractions and closures
The hamiltonian index of a graph is the smallest integer such that the -th iterated line graph of is hamiltonian. We first show that, with one exceptional case, adding an edge to a graph cannot increase its hamiltonian index. We use this result to prove that neither the contraction of an -contractible subgraph of a graph nor the closure operation performed on (if is claw-free) affects the value of the hamiltonian index of a graph
Formal Derivation of Concurrent Garbage Collectors
Concurrent garbage collectors are notoriously difficult to implement
correctly. Previous approaches to the issue of producing correct collectors
have mainly been based on posit-and-prove verification or on the application of
domain-specific templates and transformations. We show how to derive the upper
reaches of a family of concurrent garbage collectors by refinement from a
formal specification, emphasizing the application of domain-independent design
theories and transformations. A key contribution is an extension to the
classical lattice-theoretic fixpoint theorems to account for the dynamics of
concurrent mutation and collection.Comment: 38 pages, 21 figures. The short version of this paper appeared in the
Proceedings of MPC 201
Quantifying Triadic Closure in Multi-Edge Social Networks
Multi-edge networks capture repeated interactions between individuals. In
social networks, such edges often form closed triangles, or triads. Standard
approaches to measure this triadic closure, however, fail for multi-edge
networks, because they do not consider that triads can be formed by edges of
different multiplicity. We propose a novel measure of triadic closure for
multi-edge networks of social interactions based on a shared partner statistic.
We demonstrate that our operalization is able to detect meaningful closure in
synthetic and empirical multi-edge networks, where common approaches fail. This
is a cornerstone in driving inferential network analyses from the analysis of
binary networks towards the analyses of multi-edge and weighted networks, which
offer a more realistic representation of social interactions and relations.Comment: 19 pages, 5 figures, 6 table
A search method for thin positions of links
We give a method for searching for thin positions of a given link.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-42.abs.htm
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