
Steiner Tree in kstar Caterpillar Convex Bipartite Graphs – A Dichotomy
The class of kstar caterpillar convex bipartite graphs generalizes the ...
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Compacting Frequent Star Patterns in RDF Graphs
Knowledge graphs have become a popular formalism for representing entiti...
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Star transposition Gray codes for multiset permutations
Given integers k≥ 2 and a_1,…,a_k≥ 1, let a:=(a_1,…,a_k) and n:=a_1+⋯+a_...
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Empirical Analysis of Common Subgraph Isomorphism Approaches to the LostinSpace Star Identification Problem
The process of identifying stars is integral toward stellar based orient...
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Oriented Diameter of Star Graphs
An orientation of an undirected graph G is an assignment of exactly one...
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Star sampling with and without replacement
Star sampling (SS) is a random sampling procedure on a graph wherein eac...
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Data Management in TimeDomain Astronomy: Requirements and Challenges
In timedomain astronomy, we need to use the relational database to mana...
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Intersection graph of maximal stars
A biclique of a graph G is an induced complete bipartite subgraph of G such that neither part is empty. A star is a biclique of G such that one part has exactly one vertex. The star graph of G is the intersection graph of the maximal stars of G. A graph H is starcritical if its star graph is different from the star graph of any of its proper induced subgraphs. We begin by presenting a bound on the size of starcritical preimages by a quadratic function on the number of vertices of the star graph, then proceed to describe a Krausztype characterization for this graph class; we combine these results to show membership of the recognition problem in NP. We also present some properties of star graphs. In particular, we show that they are biconnected, that every edge belongs to at least one triangle, characterize the structures the preimage must have in order to generate degree two vertices, and bound the diameter of the star graph with respect to the diameter of its preimage. Finally, we prove a monotonicity theorem, which we apply to list every star graph on at most eight vertices.
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