Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Comparing Upper Broadcast Domination and Boundary Independence Numbers
  of Graphs   A broadcast on a nontrivial connected graph G with vertex set V is a function
f from V to {0,1,...,diam(G)} such that f(v) is at most the eccentricity of v
for all v in V. The weight of f is the sum of the function values taken over V.
A vertex u hears f from v if f(v) is positive and d(u,v) is at most f(v). A
broadcast f is dominating if every vertex of G hears f. The upper broadcast
number of G is {\Gamma}_{b}(G), which is the maximum weight of a minimal
dominating broadcast on G. A broadcast f is boundary independent if, for any
vertex w that hears f from vertices v_{1},...,v_{k}, where k is at least 2, the
distance d(w,v_{i}) equals f(v_{i}) for each i. The maximum weight of a
boundary independent broadcast is the boundary independence broadcast number
{\alpha}_{bn}(G). We compare {\alpha}_{bn} to {\Gamma}_{b}, showing that
neither is an upper bound for the other. We show that the differences
{\Gamma}_{b}-{\alpha}_{bn} and {\alpha}_{bn}-{\Gamma}_{b} are unbounded, the
ratio {\alpha}_{bn}/{\Gamma}_{b} is bounded for all graphs, and
{\Gamma}_{b}/{\alpha}_{bn} is bounded for bipartite graphs but unbounded in
general.

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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph