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Abstract:

Circular-arc graphs are the intersection graphs of open arcs on a circle. Circle graphs are the intersection graphs of chords on a circle. These graph classes have been the subject of much study for many years and numerous interesting results have been reported. Many subclasses of both circular-arc graphs and circle graphs have been defined and different characterizations formulated. In this survey, we summarize the most important structural results related to circular-arc graphs and circle graphs and present the main open problems. © 2013 Elsevier B.V. All rights reserved.

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Documento: Artículo
Título:Structural results on circular-arc graphs and circle graphs: A survey and the main open problems
Autor:Durán, G.; Grippo, L.N.; Safe, M.D.
Filiación:CONICET, Argentina
Departamento de Matemática, Instituto de Cálculo, Universidad de Buenos Aires, Buenos Aires, Argentina
Departamento de Ingeniería Industrial, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago, Chile
Instituto de Ciencias, Universidad Nacional de General Sarmiento, Los Polvorines, Argentina
Palabras clave:Circle graphs; Circular-arc graphs; Forbidden subgraph characterizations; Interval graphs; Matrix characterizations; Permutation graphs
Año:2014
Volumen:164
Número:PART 2
Página de inicio:427
Página de fin:443
DOI: http://dx.doi.org/10.1016/j.dam.2012.12.021
Título revista:Discrete Applied Mathematics
Título revista abreviado:Discrete Appl Math
ISSN:0166218X
CODEN:DAMAD
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0166218X_v164_nPART2_p427_Duran

Referencias:

  • Alcón, L., Cerioli, M., Herrera De Figueiredo, C., Gutierrez, M., Meidanis, J., Tree loop graphs (2007) Discrete Mathematics, 155, pp. 686-694
  • Bang-Jensen, J., Locally semicomplete digraphs: A generalization of tournaments (1990) Journal of Graph Theory, 14, pp. 371-390
  • Bang-Jensen, J., Hell, P., On chordal proper circular arc graphs (1994) Discrete Mathematics, 128, pp. 395-398
  • Bonomo, F., Durán, G., Grippo, L., Safe, M., Partial characterizations of circular-arc graphs (2009) Journal of Graph Theory, 61, pp. 289-306
  • Bonomo, F., Durán, G., Grippo, L., Safe, M., Partial characterizations of circle graphs (2010) Discrete Applied Mathematics, 159, pp. 1699-1706
  • Bouchet, A., Reducing prime graphs and recognizing circle graphs (1987) Combinatorica, 7, pp. 243-254
  • Bouchet, A., Unimodularity and circle graphs (1987) Discrete Mathematics, 66, pp. 203-208
  • Bouchet, A., Circle graphs obstructions (1994) Journal of Combinatorial Theory. Series B, 60, pp. 107-144
  • Bouchet, A., Bipartite graphs that are not circle graphs (1999) Université de Grenoble. Annales de l'Institut Fourier, 49, pp. 809-814
  • Chong-Keang, L., Yee-Hock, P., On graphs without multicliqual edges (1981) Journal of Graph Theory, 5, pp. 443-451
  • Chudnovsky, M., Kapadia, R., Detecting a theta or a prism (2008) SIAM Journal on Discrete Mathematics, 22, pp. 1164-1186
  • Chudnovsky, M., Seymour, P., The structure of claw-free graphs (2005) London Mathematical Society Lecture Note Series, 327, pp. 153-171
  • Confessore, G., Dell'Olmo, P., Giordani, S., An approximation result for a periodic allocation problem (2001) Discrete Applied Mathematics, 112, pp. 53-72
  • Conforti, M., (K 4 - e) -free graphs and star cutsets (1989) Lecture Notes in Mathematics, 1403, pp. 236-253
  • Cunningham, W.H., Decomposition of directed graphs (1982) SIAM Journal on Algebraic and Discrete Methods, 3, pp. 214-228
  • Daligault, J., Gonçalves, D., Rao, M., Diamond-free circle graphs are Helly circle (2010) Discrete Mathematics, 310, pp. 845-849
  • De Fraysseix, H., A characterization of circle graphs (1984) European Journal of Combinatorics, 5, pp. 223-238
  • Durán, G., (2000) Sobre Grafos Intersección de Arcos y Cuerdas en un Círculo (In Spanish), , Ph.D. thesis, Departmento de Computación, FCEyN, Universidad de Buenos Aires, Buenos Aires
  • Durán, G., Some new results on circle graphs (2003) Matemática Contemporânea, 25, pp. 91-106
  • Durán, G., Gravano, A., McConnell, R., Spinrad, J., Tucker, A., Polynomial time recognition of unit circular-arc graphs (2006) Journal of Algorithms, 58, pp. 67-78
  • Even, S., Itai, A., Queues, stacks and graphs (1971) Theory of Machines and Computations, pp. 71-86. , A. Kohavi, A. Paz, Academic Press New York
  • Even, S., Pnueli, A., Lempel, A., Permutation graphs and transitive graphs (1972) Journal of the ACM, 19, pp. 400-410
  • Feder, T., Hell, P., Huang, J., List homomorphisms and circular-arc graphs (1999) Combinatorica, 19, pp. 487-505
  • Francis, M., Hell, P., Stacho, J., (2012) Obstructions to Chordal Circular-arc Graphs, , Manuscript
  • Fulkerson, D., Gross, O., Incidence matrices and interval graphs (1965) Pacific Journal of Mathematics, 15, pp. 835-855
  • Gabor, C., Supowit, K., Hsu, W., Recognizing circle graphs in polynomial time (1989) Journal of the ACM, 36, pp. 435-473
  • Gallai, T., Transitiv orientierbare Graphen (1967) Acta Mathematica Academiae Scientiarum Hungaricae, 18, pp. 25-66
  • Garey, M., Johnson, D., Miller, G., Papadimitriou, C., The complexity of coloring circular arcs and chords (1980) SIAM Journal on Algebraic and Discrete Methods, 1, pp. 216-227
  • Gasse, E., A proof of a circle graph characterization (1997) Discrete Mathematics, 173, pp. 277-283
  • Gavril, F., Algorithms for a maximum clique and a maximum independent set of a circle graph (1973) Networks, 3, pp. 261-273
  • Geelen, J., Oum, S., Circle graph obstructions under pivoting (2009) Journal of Graph Theory, 61, pp. 1-11
  • Giakoumakis, V., Roussel, F., Thuillier, H., On P 4-tidy graphs (1997) Discrete Mathematics & Theoretical Computer Science, 1, pp. 17-41
  • Golumbic, M., (2004) Algorithmic Graph Theory and Perfect Graphs, 57. , second ed. Annals of Discrete Mathematics North-Holland Amsterdam
  • Golumbic, M.C., Goss, C.F., Perfect elimination and chordal bipartite graphs (1978) Journal of Graph Theory, 2, pp. 155-163
  • Grippo, L.N., Safe, M.D., On circular-arc graphs having a model with no three arcs covering the circle (2012) Proceedings of the XVI Congreso Latino-Iberoamericano de Investigaciøn Operativa (CLAIO), , held in Rio de Janeiro, Brazil, September 24-28
  • Hadwiger, H., Debrunner, H., Klee, V., (1964) Combinatorial Geometry in the Plane, , Holt Rineharot and Winston New York
  • Hell, P., Huang, J., Lexicographic orientation and representation algorithms for comparability graphs, proper circular arc graphs, and proper interval graphs (1995) Journal of Graph Theory, 20, pp. 361-374
  • Hell, P., Huang, J., Two remarks on circular-arc graphs (1997) Graphs and Combinatorics, 13, pp. 65-72
  • Hell, P., Huang, J., Interval bigraphs and circular arc graphs (2004) Journal of Graph Theory, 46, pp. 313-327
  • Hoàng, C., (1985) Perfect Graphs, , Ph.D. Thesis, School of Computer Science, McGill University, Montreal
  • Jamison, B., Olariu, S., A new class of brittle graphs (1989) Studies in Applied Mathematics, 81, pp. 89-92
  • Jamison, B., Olariu, S., On a unique tree representation for P 4-extendible graphs (1991) Discrete Applied Mathematics, 34, pp. 151-164
  • Joeris, B.L., Lin, M.C., McConnell, R.M., Spinrad, J.P., Szwarcfiter, J.L., Linear-time recognition of Helly circular-arc models and graphs (2011) Algorithmica, 59, pp. 215-239
  • Klee, V., What are the intersection graphs of arcs in a circle? (1969) The American Mathematical Monthly, 76, pp. 810-813
  • Kloks, T., Kratsch, D., Müller, H., Dominoes (1995) Lecture Notes in Computer Science, 93, pp. 106-120
  • Köhler, E.G., (1999) Graphs Without Asteroidal Triples, , Ph.D. Thesis, Tecnischen Universität Berlin, Berlin, Germany
  • Lekkerkerker, C., Boland, D., Representation of finite graphs by a set of intervals on the real line (1962) Fundamenta Mathematicae, 51, pp. 45-64
  • Lévêque, B., Lin, D., Maffray, F., Trotignon, N., Detecting induced subgraphs (2007) Electronic Notes in Discrete Mathematics, 29, pp. 207-211
  • Lin, M.C., Soulignac, F., Szwarcfiter, J.L., Proper Helly circular-arc graphs (2007) Proceedings of the 33th International Workshop on Graph Theoretic Concepts in Computer Science, 4769, pp. 248-257. , WG'07, Dornburg, Germany, 2007 Lectures Notes in Computer Science
  • Lin, M., Szwarcfiter, J., Characterizations and linear time recognition of Helly circular-arc graphs (2006) Lecture Notes in Computer Science, 4112, pp. 73-82
  • Lin, M.C., Szwarcfiter, J.L., Efficient construction of unit circular-arc models (2006) Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 309-315. , SODA'06, held in Miami, Florida, USA, January 22-26, 2006 SIAM
  • Lin, M.C., Szwarcfiter, J.L., Characterizations and recognition of circular-arc graphs and subclasses: A survey (2009) Discrete Mathematics, 309, pp. 5618-5635
  • McConnell, R., Linear-time recognition of circular-arc graphs (2003) Algorithmica, 37, pp. 93-147
  • Naji, W., Reconnaissance des graphes de cordes (1985) Discrete Mathematics, 54, pp. 329-337
  • Olariu, S., Paw-free graphs (1988) Information Processing Letters, 28, pp. 53-54
  • Oxley, J., (2011) Matroid Theory, , Oxford
  • Parthasarathy, K., Ravindra, G., The strong perfect-graph conjecture is true for K 1 , 3-free graphs (1976) Journal of Combinatorial Theory. Series B, 21, pp. 212-223
  • Paul, C., (2006) Aspects Algorithmiques de la Décomposition Modulaire, , Ph.D. Thesis, CNRS - LIRMM - Université Montpellier, Montpellier
  • Proskurowski, A., Telle, J.A., Classes of graphs with restricted interval models (1999) Discrete Mathematics & Theoretical Computer Science, pp. 167-176
  • Roberts, F., Indifference graphs (1969) Proof Techniques in Graph Theory, pp. 139-146. , F. Harary, Academic Press
  • Skrien, D.J., A relationship between triangulated graphs, comparability graphs, proper interval graphs, proper circular arc graphs, and nested interval graphs (1982) Journal of Graph Theory, 6, pp. 309-316
  • Spinrad, J., Circular-arc graphs with clique cover number two (1988) Journal of Combinatorial Theory. Series B, 44, pp. 300-306
  • Spinrad, J., Recognition of circle graphs (1994) Journal of Algorithms, 16, pp. 264-282
  • Tinhofer, G., Strong tree-cographs are Birkoff graphs (1989) Discrete Applied Mathematics, 22, pp. 275-288
  • Trotter, W., Moore, J., Characterization problems for graphs, partially ordered sets, lattices, and families of sets (1976) Discrete Mathematics, 16, pp. 361-381
  • Tucker, A., (1969) Two Characterizations of Proper Circular-arc Graphs, , Ph.D. Thesis, Stanford Operations Research Department
  • Tucker, A., Characterizing circular-arc graphs (1970) Bulletin of the American Mathematical Society, 76, pp. 1257-1260
  • Tucker, A., Matrix characterizations of circular-arc graphs (1971) Pacific Journal of Mathematics, 38, pp. 535-545
  • Tucker, A., Structure theorems for some circular-arc graphs (1974) Discrete Mathematics, 7, pp. 167-195
  • Tucker, A., An efficient test for circular-arc graphs (1980) SIAM Journal on Computing, 9, pp. 1-24
  • Tucker, A., Coloring perfect (K 4 - e) -free graphs (1987) Journal of Combinatorial Theory. Series B, 42, pp. 313-318
  • Wegner, G., (1967) Eigenschaften der Nerven Homologisch-einfacher Familien im Rn, , Ph.D. Thesis, Georg-August-Universität zu Göttingen

Citas:

---------- APA ----------
Durán, G., Grippo, L.N. & Safe, M.D. (2014) . Structural results on circular-arc graphs and circle graphs: A survey and the main open problems. Discrete Applied Mathematics, 164(PART 2), 427-443.
http://dx.doi.org/10.1016/j.dam.2012.12.021
---------- CHICAGO ----------
Durán, G., Grippo, L.N., Safe, M.D. "Structural results on circular-arc graphs and circle graphs: A survey and the main open problems" . Discrete Applied Mathematics 164, no. PART 2 (2014) : 427-443.
http://dx.doi.org/10.1016/j.dam.2012.12.021
---------- MLA ----------
Durán, G., Grippo, L.N., Safe, M.D. "Structural results on circular-arc graphs and circle graphs: A survey and the main open problems" . Discrete Applied Mathematics, vol. 164, no. PART 2, 2014, pp. 427-443.
http://dx.doi.org/10.1016/j.dam.2012.12.021
---------- VANCOUVER ----------
Durán, G., Grippo, L.N., Safe, M.D. Structural results on circular-arc graphs and circle graphs: A survey and the main open problems. Discrete Appl Math. 2014;164(PART 2):427-443.
http://dx.doi.org/10.1016/j.dam.2012.12.021