On the bend number of circular-arc graphs as edge intersection graphs of paths on a grid

Golumbic, Lipshteyn and Stern proved that every graph can be represented as the edge intersection graph of paths on a grid, i.e., one can associate to each vertex of the graph a nontrivial path on a grid such that two vertices are adjacent if and only if the corresponding paths share at least one ed...

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Autor principal: Alcón, L.
Otros Autores: Bonomo, F., Durán, G., Gutierrez, M., Pía Mazzoleni, M., Ries, B., Valencia-Pabon, M.
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: Elsevier 2015
Acceso en línea:Registro en Scopus
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100 1 |a Alcón, L. 
245 1 3 |a On the bend number of circular-arc graphs as edge intersection graphs of paths on a grid 
260 |b Elsevier  |c 2015 
506 |2 openaire  |e Política editorial 
504 |a Asinowski, A., Ries, B., Some properties of edge intersection graphs of single-bend paths on a grid (2012) Discrete Math., 312, pp. 427-440 
504 |a Asinowski, A., Suk, A., Edge intersection graphs of systems of paths on a grid with a bounded number of bends (2009) Discrete Appl. Math., 157, pp. 3174-3180 
504 |a Biedl, T., Stern, M., On edge intersection graphs of k-bend paths in grids (2010) Discrete Math. Theoret. Comput. Sci., 12, pp. 1-12 
504 |a Bondy, J., Murty, U., (2007) Graph Theory, , Springer, New York 
504 |a Cao, Y., Grippo, L., Safe, M., Forbidden induced subgraphs of normal Helly circular-arc graphs: Characterization and detection, , arxiv:1405.0329v1 
504 |a Durán, G., Grippo, L., Safe, M., Structural results on circular-arc graphs and circle graphs: a survey and the main open problems (2014) Discrete Appl. Math., 164, pp. 427-443 
504 |a Epstein, D., Golumbic, M., Morgenststern, G., Approximation algorithms for B1-EPG graphs (2013) Lect. Notes Comput. Sci., 8037, pp. 328-340 
504 |a Francis, M., Hell, P., Stacho, J., Forbidden structure characterization of circular-arc graphs and a certifying recognition algorithm, , arxiv:1408.2639v1 
504 |a Gavril, F., Algorithms on circular-arc graphs (1974) Networks, 4, pp. 357-369 
504 |a Golumbic, M., Lipshteyn, M., Stern, M., Edge intersection graphs of single bend paths on a grid (2009) Networks, 54, pp. 130-138 
504 |a Lin, M., Soulignac, F., Szwracfiter, J., Normal Helly circular-arc graphs and its subclasses (2013) Discrete Appl. Math., 161, pp. 1037-1059 
504 |a Lin, M., Szwarcfiter, J., Characterizations and recognition of circular-arc graphs and subclasses: A survey (2009) Discrete Math., 309, pp. 5618-5635 
504 |a Tucker, A., Characterizing circular-arc graphs (1970) Bull. Amer. Math. Soc., 76, pp. 1257-1260 
520 3 |a Golumbic, Lipshteyn and Stern proved that every graph can be represented as the edge intersection graph of paths on a grid, i.e., one can associate to each vertex of the graph a nontrivial path on a grid such that two vertices are adjacent if and only if the corresponding paths share at least one edge of the grid. For a nonnegative integer k, Bk-EPG graphs are defined as graphs admitting a model in which each path has at most k bends. Circular-arc graphs are intersection graphs of open arcs of a circle. It is easy to see that every circular-arc graph is B4-EPG, by embedding the circle into a rectangle of the grid. In this paper we prove that every circular-arc graph is B3-EPG, but if we restrict ourselves to rectangular representations there exist some graphs that require paths with four bends. We also show that normal circular-arc graphs admit rectangular representations with at most two bends per path. Moreover, we characterize graphs admitting a rectangular representation with at most one bend per path by forbidden induced subgraphs, and we show that they are a subclass of normal Helly circular-arc graphs. © 2015 Elsevier B.V.  |l eng 
536 |a Detalles de la financiación: Fondo Nacional de Desarrollo Científico, Tecnológico y de Innovación Tecnológica, 1140787 
536 |a Detalles de la financiación: Secretaría de Ciencia y Técnica, Universidad de Buenos Aires, 20020130100808BA 
536 |a Detalles de la financiación: 13MATH-07 
536 |a Detalles de la financiación: 112-200901-00178, 112-201201-00450CO, PIP 122-01001-00310 
536 |a Detalles de la financiación: Agencia Nacional de Promoción Científica y Tecnológica, 2012-1324, PICT 2010-1970 
536 |a Detalles de la financiación: E-mail addresses: liliana@mate.unlp.edu.ar; fbonomo@dc.uba.ar; gduran@dm.uba.ar; marisa@mate.unlp.edu.ar; pia@mate.unlp.edu.ar; bernard.ries@dauphine.fr; valencia@lipn.univ-paris13.fr. This work was partially supported by MathAmSud Project 13MATH-07 (Argentina–Brazil– Chile–France), UBACyT Grant 20020130100808BA, CONICET PIP 122-01001-00310, 112-200901-00178 and 112-201201-00450CO and ANPCyT PICT 2010-1970 and 2012-1324 (Argentina), FONDECyT Grant 1140787 and Millennium Science Institute “Complex Engineering Systems” (Chile). 
593 |a Dto. de Matemática, FCE-UNLP, La Plata, Argentina 
593 |a Dto. de Computación, FCEN-UBA, Buenos Aires, Argentina 
593 |a Dto. de Matemática e Inst. de Cálculo, FCEN-UBA, Buenos Aires, Argentina 
593 |a Dto. de Ingeniería Industrial, FCFM-Univ. de Chile, Santiago, Chile 
593 |a Université Paris-Dauphine, LAMSADE, Paris, France 
593 |a Université Paris-13, Sorbonne Paris Cité LIPN, CNRS UMR7030, Villetaneuse, France 
593 |a Délégation at the INRIA Nancy - Grand Est, France 
593 |a CONICET, Argentina 
690 1 0 |a (NORMAL, HELLY) 
690 1 0 |a CIRCULAR-ARC GRAPHS 
690 1 0 |a EDGE INTERSECTION GRAPHS 
690 1 0 |a FORBIDDEN INDUCED SUBGRAPHS 
690 1 0 |a PATHS ON A GRID 
700 1 |a Bonomo, F. 
700 1 |a Durán, G. 
700 1 |a Gutierrez, M. 
700 1 |a Pía Mazzoleni, M. 
700 1 |a Ries, B. 
700 1 |a Valencia-Pabon, M. 
773 0 |d Elsevier, 2015  |g v. 50  |h pp. 249-254  |p Electron. Notes Discrete Math.  |x 15710653  |t Electronic Notes in Discrete Mathematics 
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