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On the bend number of circular-arc graphs as edge intersection graphs of paths on a grid
(Elsevier B.V., 2018)
Golumbic, Lipshteyn and Stern [12] proved that every graph can be represented as the edge
intersection graph of paths on a grid (EPG graph), i.e., one can associate with each vertex
of the graph a nontrivial path on a ...
Vertex Intersection Graphs of Paths on a Grid: Characterization Within Block Graphs
(Springer Tokyo, 2017-07)
We investigate graphs that can be represented as vertex intersections of horizontal and vertical paths in a grid, the so called B0-VPG graphs. Recognizing this class is an NP-complete problem. Although, there exists a ...
Optimal grid representations
(Wiley Subscription Services, Inc., A Wiley CompanyEstados UnidosInstituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa de EngenhariaInstituto Tércio Pacitti de Aplicações e Pesquisas Computacionais, 2017)
On PVPG graphs: a subclass of vertex intersection graphs of paths on a grid
(Sociedade Brasileira de Matemática, 2021-10)
In this paper, we study the class of PVPG graphs, this is a subclass of VPG graphs such that all the representing paths are between two parallel lines of the grid and have their endpoints on these lines. We prove that PVPG ...
On the bend number of circular-arc graphs as edge intersection graphs of paths on a grid
(Elsevier Science, 2018-01)
Golumbic, Lipshteyn and Stern [12] proved that every graph can be represented as the edge intersection graph of paths on a grid (EPG graph), i.e., one can associate with each vertex of the graph a nontrivial path on a ...
Exploiting direction in grid graphs to build a fast and lighter subgoal graph
(2022)
En el problema de path planning sobre grafos tipo grilla, una de las principales técnicas de preprocesamiento del estado del arte son los subgoal graphs. Estos grafos consisten en un subconjunto de nodos importantes ...
Clique coloring B1-EPG graphs
(Elsevier, 2017)
We consider the problem of clique coloring, that is, coloring the vertices of a given graph such that no (maximal) clique of size at least two is monocolored. It is known that interval graphs are 2-clique colorable. In ...