A note on Helly-B1-EPG graphs
Edge intersection graphs of paths on a grid (EPG graphs) aregraphs whose vertices can be represented as nontrivial paths on agrid such that two vertices are adjacent if and only if the corresponding paths share at least one edge of the grid. When the paths haveat most one change of direction (bend)...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/160294 |
| Acceso en línea: | http://hdl.handle.net/11336/160294 |
| Access Level: | acceso abierto |
| Palabra clave: | EDGE- INYTERSECTION GRAPHS OF PATHS ON A GRID HELLY PROPERTY SINGLE BEND PATHS https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | Edge intersection graphs of paths on a grid (EPG graphs) aregraphs whose vertices can be represented as nontrivial paths on agrid such that two vertices are adjacent if and only if the corresponding paths share at least one edge of the grid. When the paths haveat most one change of direction (bend) these graphs are called B1-EPG graphs. In this paper, we delimit some subclasses of B1-EPGgraphs that admit a Helly-B1-EPG representation. It is known thatB1-EPG and Helly-B1-EPG are hereditary classes, so they can becharacterized by forbidden structures. In both cases, finding thewhole list of minimal forbidden induced subgraphs are challengingopen problems. Taking a step towards solving those problems, wedescribe a few structures at least one of which will necessarily bepresent in any B1-EPG graph that does not admit a Helly representation. In addition, we show that the well known families of Blockgraphs, Cactus and Line of Bipartite graphs are totally contained inthe class Helly-B1-EPG. |
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