469 research outputs found
Characterizing Block Graphs in Terms of their Vertex-Induced Partitions
Given a finite connected simple graph with vertex set and edge
set , we will show that
the (necessarily unique) smallest block graph with vertex set whose
edge set contains is uniquely determined by the -indexed family of the various partitions
of the set into the set of connected components of the
graph ,
the edge set of this block graph coincides with set of all -subsets
of for which and are, for all , contained
in the same connected component of ,
and an arbitrary -indexed family of
partitions of the set is of the form for some
connected simple graph with vertex set as above if and only if,
for any two distinct elements , the union of the set in
that contains and the set in that contains coincides with
the set , and holds for all .
As well as being of inherent interest to the theory of block graphs, these
facts are also useful in the analysis of compatible decompositions and block
realizations of finite metric spaces
Blocks and Cut Vertices of the Buneman Graph
Given a set \Sg of bipartitions of some finite set of cardinality at
least 2, one can associate to \Sg a canonical -labeled graph \B(\Sg),
called the Buneman graph. This graph has several interesting mathematical
properties - for example, it is a median network and therefore an isometric
subgraph of a hypercube. It is commonly used as a tool in studies of DNA
sequences gathered from populations. In this paper, we present some results
concerning the {\em cut vertices} of \B(\Sg), i.e., vertices whose removal
disconnect the graph, as well as its {\em blocks} or 2-{\em connected
components} - results that yield, in particular, an intriguing generalization
of the well-known fact that \B(\Sg) is a tree if and only if any two splits
in \Sg are compatible
Viewing time affects overspecification:Evidence for two strategies of attribute selection during reference production
Speakers often produce definite referring expressions that are overspecified: they tend to include more attributes than necessary to distinguish the target referent. The current paper investigates how the occurrence of overspecification is affected by viewing time. We conducted an experiment in which speakers were asked to refer to target objects in visual domains. Half of the speakers had unlimited time to inspect the domains, while viewing time was limited (1000 ms) for the other half. The results reveal that limited viewing time induces the occurrence of overspecification. We conjecture that limited viewing time caused speakers to rely heavily on quick heuristics during attribute selection, which urge them to select attributes that are perceptually salient. In the case of unlimited inspection time, speakers seem to rely on a combination of heuristic and more deliberate selection strategies
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