
Proper circular arc graphs as intersection graphs of paths on a grid
In this paper we present a characterisation, by an infinite family of mi...
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On vertexedge and independent vertexedge domination
Given a graph G = (V,E), a vertex u ∈ V vedominates all edges incident ...
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Fiedler vector analysis for particular cases of connected graphs
In this paper, some subclasses of block graphs are considered in order t...
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Constructions of betweennessuniform graphs from trees
Betweenness centrality is a measure of the importance of a vertex x insi...
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Linear Time Construction of Indexable Founder Block Graphs
We introduce a compact pangenome representation based on an optimal segm...
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SplitDecomposition Trees with Prime Nodes: Enumeration and Random Generation of Cactus Graphs
In this paper, we build on recent results by Chauve et al. (2014) and Ba...
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Minimum Number of Bends of Paths of Trees in a Grid Embedding
We are interested in embedding trees T with maximum degree at most four ...
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B1EPG representations using blockcutpoint trees
In this paper, we are interested in the edge intersection graphs of paths of a grid where each path has at most one bend, called B1EPG graphs and first introduced by Golumbic et al (2009). We also consider a proper subclass of B1EPG, the LEPG graphs, which allows paths only in “L” shape. We show that two superclasses of trees are B1EPG (one of them being the cactus graphs). On the other hand, we show that the block graphs are LEPG and provide a linear time algorithm to produce LEPG representations of generalization of trees. These proofs employed a new technique from previous results in the area based on blockcutpoint trees of the respective graphs.
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