Results 1 to 10 of about 137,225 (153)
Representations of Edge Intersection Graphs of Paths in a Tree [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 Let $\mathcal{P}$ be a collection of nontrivial simple paths in a tree $T$. The edge intersection graph of $\mathcal{P}$, denoted by EPT($\mathcal{P}$), has vertex set that corresponds to the members of $\mathcal{P}$, and two vertices are joined by an ...
Martin Charles Golumbic +2 more
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On edge intersection graphs of paths with 2 bends [PDF]
Discrete Applied Mathematics, 2017 An EPG-representation of a graph G is a collection of paths in a grid, each corresponding to a single vertex of G, so that two vertices are adjacent if and only if their corresponding paths share infinitely many points.
Martin Pergel, Paweł Rzążewski
core +6 more sources
Edge intersection graphs of
Discrete Applied Mathematics, 2015 In this paper we continue the study of the edge intersection graphs of one (or zero) bend paths on a rectangular grid. That is, the edge intersection graphs where each vertex is represented by one of the following shapes: $\llcorner$,$\ulcorner ...
Kathie Cameron +2 more
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On edge-intersection graphs of k-bend paths in grids [PDF]
Discrete Mathematics & Theoretical Computer Science, 2010 Edge-intersection graphs of paths in grids are graphs that can be represented such that vertices are paths in a grid and edges between vertices of the graph exist whenever two grid paths share a grid edge. This type of graphs is motivated by applications
Therese Biedl, Michal Stern
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Graphs of Edge-Intersecting Non-Splitting Paths in a Tree: Representations of Holes-Part II [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 Given a tree and a set P of non-trivial simple paths on it, VPT(P) is the VPT graph (i.e. the vertex intersection graph) of the paths P, and EPT(P) is the EPT graph (i.e. the edge intersection graph) of P.
Arman Boyacı +3 more
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On the j-Edge Intersection Graph of Cycle Graph
European Journal of Pure and Applied Mathematics, 2023 This paper defines a new class of graphs using the spanning subgraphs of a cycle graph as vertices. This class of graphs is called $j$-edge intersection graph of cycle graph, denoted by $E_{C_{(n,j)}}$. The vertex set of $E_{C_{(n,j)}}$ is the set of spanning subgraphs of cycle graph with $j$ edges where $n \geq 3$ and $j$ is a nonnegative integer such
Jhon Cris Bonifacio +2 more
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Edge Intersection Graphs of Paths on a Triangular Grid [PDF]
Anais do VII Encontro de Teoria da Computação (ETC 2022), 2022 19 pages, 12 ...
Vitor Tocci F. de Luca +3 more
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On Superperfection of Edge Intersection Graphs of Paths
, 2020 The Routing and Spectrum Assignment problem in Flexgrid Elastic Optical Networks can be modeled in two phases: a selection of paths in the network and an interval coloring problem in the edge-intersection graph of these paths. The interval chromatic number equals the smallest size of a spectrum such that a proper interval coloring is possible, the ...
Hervé Kerivin, Annegret K. Wagler
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The Complexity of Helly-$B_{1}$ EPG Graph Recognition [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 Golumbic, Lipshteyn, and Stern defined in 2009 the class of EPG graphs, the intersection graph class of edge paths on a grid. An EPG graph $G$ is a graph that admits a representation where its vertices correspond to paths in a grid $Q$, such that two ...
Claudson F. Bornstein +4 more
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On $k$-Bend and Monotonic $\ell$-Bend Edge Intersection Graphs of Paths on a Grid [PDF]
, 2020 If a graph $G$ can be represented by means of paths on a grid, such that each vertex of $G$ corresponds to one path on the grid and two vertices of $G$ are adjacent if and only if the corresponding paths share a grid edge, then this graph is called EPG and the representation is called EPG representation.
Eranda Çela, Elisabeth Gaar
+9 more sources