Flavia Bonomo-Braberman

On the b-Coloring of Cographs and P4-Sparse Graphs

2009, Graphs and Combinatorics 25 (2), 153-167, 2009
Citas: 82
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Autor(es)

Flavia Bonomo and Guillermo Durán and Frederic Maffray and Javier Marenco and Mario Valencia-Pabon

Abstract

A b-coloring of a graph is a coloring such that every color class admits a vertex adjacent to at least one vertex receiving each of the colors not assigned to it. The b-chromatic number of a graph G, denoted by χ b (G), is the maximum number t such that G admits a b-coloring with t colors. A graph G is b-continuous if it admits a b-coloring with t colors, for every . We define a graph G to be b-monotonic if χ b (H 1) ≥ χ b (H 2) for every induced subgraph H 1 of G, and every induced subgraph H 2 of H 1. In this work, we prove that P 4-sparse graphs (and, in particular, cographs) are b-continuous and b-monotonic. Besides, we describe a dynamic programming algorithm to compute the b-chromatic number in polynomial time within these graph classes.

Plot de citas

Citas

# Title Year Source Authors
1 The b-chromatic number of cubic graphs 2010 Graphs and Combinatorics M Jakovac, S Klavžar
2 On the b-chromatic number of regular graphs 2011 Discrete Applied Mathematics S Cabello, M Jakovac
3 The b-chromatic number and related topics—a survey 2018 Discrete Applied Mathematics M Jakovac, I Peterin
4 The b-chromatic index of graphs 2015 Discrete … VA Campos, CV Lima, NA Martins, L Sampaio
5 The b-chromatic number of corona graphs 2012 Utilitas Mathematica T Nadu
6 Bounded Width Graph Classes in Parameterized Algorithms 2020 NA L Jaffke
7 On the b-coloring of P4-tidy graphs 2011 Discrete Applied Mathematics CIB Velasquez, F Bonomo, I Koch
8 On the b-chromatic number of regular graphs without 4-cycle 2012 Discrete Applied Mathematics S Shaebani
9 b-coloring of Kneser graphs 2012 Discrete applied mathematics R Balakrishnan, T Kavaskar
10 b-Coloring Parameterized by Clique-Width 2024 Theory of Computing Systems L Jaffke, PT Lima, D Lokshtanov
11 The b-chromatic index of direct product of graphs 2015 Discrete Applied Mathematics I Koch, I Peterin
12 Structural parameterizations of b-coloring 2023 NA L Jaffke, PT Lima, R Sharma
13 b-coloring of tight graphs 2012 Discrete Applied Mathematics F Havet, CL Sales, L Sampaio
14 On b-colorings and b-continuity of graphs 2012 NA M Alkhateeb
15 The b-chromatic number of some tree-like graphs 2010 NA ASF da Silva
16 Algorithmic aspects of graph colourings heuristics 2012 NA L Sampaio
17 More results on the z-chromatic number of graphs 2023 Discrete Applied Mathematics A Khaleghi, M Zaker
18 New bounds for the b-chromatic number of vertex deleted graphs 2022 Discrete Applied Mathematics RR Del-Vecchio, M Kouider
19 On the -critical graphs 2024 Transactions on Combinatorics M Zamime
20 A Comparison of the Grundy and b-Chromatic Number of -Free Graphs 2023 Graphs and Combinatorics Z Masih, M Zaker
21 b-Chromatic sum of a graph 2015 Discrete Mathematics, Algorithms and … PC Lisna, MS Sunitha
22 On the b-coloring of tight graphs 2017 Journal of Combinatorial Optimization M Kouider, M Zamime
23 On z-coloring and -coloring of graphs as improved variants of the b-coloring 2024 arXiv preprint arXiv:2408.12951 M Zaker
24 Maximization coloring problems on graphs with few P4 2014 Discrete Applied … V Campos, C Linhares-Sales, R Sampaio
25 A Note on the b-Chromatic Number of Corona of Graphs 2015 Journal of Interconnection Networks PC Lisna, MS Sunitha
26 The b-chromatic number and f-chromatic vertex number of regular graphs 2014 Discrete Applied … A El Sahili, H Kheddouci, M Kouider
27 The b-continuity of graphs with large girth 2017 Graphs and Combinatorics CL Sales, A Silva
28 On quasi-monotonous graphs 2016 Discrete Applied Mathematics M Kouider
29 b-Chromatic Number of Subdivision Edge and Vertex Corona 2014 International Journal of … T Pathinahan, MA Arokia, D Bhuvaneswari
30 b-Coloring graphs with large girth 2012 Journal of the Brazilian Computer … V Campos, VAE de Farias, A Silva
31 -Coloring is NP-hard on Co-bipartite Graphs and Polytime Solvable on Tree-Cographs 2015 Algorithmica F Bonomo, O Schaudt, M Stein, M Valencia-Pabon
32 -coloring of Cartesian Product of Trees 2016 NA R Balakrishnan, S Francis Raj, T Kavaskar
33 The b-chromatic number of Mycielskian of some graphs 2016 International Journal of … PC Lisna, MS Sunitha
34 b-Chromatic index of graphs 2013 Electronic Notes in … CVGC Lima, NA Martins, L Sampaio, MC Santos
35 b-coloring of some bipartite graphs. 2012 Australas. J Comb. M Blidia, NI Eschouf, F Maffray
36 On the b-coloring of G− e 2015 Discrete Applied Mathematics M Zamime, M Kouider, HA Haddadène
37 A note on approximating the b-chromatic number 2013 Discrete Applied Mathematics F Galčík, J Katrenič
38 A characterization of edge b-critical graphs 2018 Discrete Applied … A Bendali-Braham, N Ikhlef-Eschouf, M Blidia
39 On b-vertex and b-edge critical graphs 2015 Opuscula Mathematica NI Eschouf, M Blidia
40 On two conjectures on b-coloring of graph products 2017 Studia Scientiarum Mathematicarum … SF Raj, T Kavaskar
41 On the b-continuity of the lexicographic product of graphs 2016 arXiv preprint arXiv:1610.03084 CL Sales, L Sampaio, A Silva
42 b-coloring of m-tight graphs 2009 Electronic Notes in Discrete Mathematics CL Sales, L Sampaio
43 b-Chromatic Sum and b-Continuity Property of Some Graphs 2021 Journal of Interconnection Networks PC Lisna, MS Sunitha
44 Algorithmes Exacts et Exponentiels pour les Problèmes NP-difficiles sur les Graphes et Hypergraphes 2014 NA C Manfred
45 Graphs with large girth are b-continuous 2016 Electronic Notes in Discrete Mathematics A Silva, CL Sales
46 b-chromatic numbers of powers of paths and cycles 2013 Discrete Applied Mathematics WH Lin, GJ Chang
47 b-continuity and the lexicographic product of graphs 2015 Electronic Notes in Discrete Mathematics CL Sales, R Vargas, L Sampaio
48 On the Complexity of Subfall Coloring of Graphs 2021 Anais do VI Encontro de Teoria da Computação D de Andrade, A Silva
49 b-colorações de grafos 2009 NA LS Rocha
50 On the b-Chromatic Sum of Mycielskian of Km, n, Kn and Cn 2020 Journal of Interconnection Networks PC Lisna, MS Sunitha
51 b-coloring of Central Graph of Triangular Snake NA rn N Ansari, RS Chandel, R Jamal
52 b-Chromatic Sum of Mycielskian of Paths 2017 Electronic Notes in Discrete Mathematics PC Lisna, MS Sunitha
53 The lexicographic product of some chordal graphs and of cographs preserves b-continuity 2017 Electronic Notes in Discrete Mathematics CL Sales, L Sampaio, A Silva
54 On the b-Continuity of the Lexicographic Product of Graphs 2017 Graphs and Combinatorics C Linhares Sales, L Sampaio, A Silva
55 The b-continuity of graphs with large girth 2 2016 arXiv preprint arXiv:1602.01298 A Silvaa, CL Salesa
56 A note on approximating the b-chromatic number NA NA F Galcıka, J Katrenica
57 b-Coloring is NP-Hard on Co-Bipartite Graphs and Polytime Solvable on Tree-Cographs 2014 … : Third International Symposium, ISCO 2014, Lisbon … M Valencia-Pabon
58 The workshop on Coverings and Colorings has been organized by DIMA-TIA, KAM and ITI on March 6th, 2009 in the lecture room S9 of School of Computer … NA NA PG Gavenciak, P Hell, P Hlinený, P Holub
59 Tópicos em b-continuidade: Operaçoes em grafos e grafos distância-hereditários 2012 NA LP Magalhães
60 HABILITATIONA DIRIGER DES RECHERCHES NA NA M VALENCIA-PABON
61 b-coloring of m-tight graphs (Full Version) NA NA CLSL Sampaio
62 Etude structurelle de quelques classes de graphes 2013 NA M Mechebbek
63 b-coloraçao de grafos com poucos P4's 2010 NA V Campos, CL Sales, A Maia, R Sampaio
64 Estudo de casos de complexidade de colorações gulosa de vértices e de arestas 2011 NA AKM Oliveira
65 Théorie des graphes, et de l'approximation pour le routage, la coloration et l'apprentissage d'équilibres. NA PRiSM/CNRS, LIX/école polytechnique J Cohen
66 Uma relaç ao entre b-coloraç ao e teoria espectral em cografos NA NA AA Jones, F Protti, RR Del-Vecchio
67 Groupes d'automorphismes associés aux colorations de graphes 2017 NA S Kerdjoudj
68 Un enfoque algorítmico sobre algunas variantes del problema de coloreo de grafos y el problema de conjunto independiente máximo 2014 NA IV Koch
69 b-coloração e b-continuidade em grafos NA NA L Pierezan, MR Cerioli
70 Le nombre b-chromatique de quelques classes de graphes généralisant les arbres 2010 NA M de Werra
71 O número b-cromático de alguns gráficos em forma de árvore 2010 NA ASF Silva
72 On b-colorings of graphs with few P4's NA NA V Campos, CL Sales, A Maia, R Sampaio
73 Graphs with large girth are b-continuous 2 NA NA A Silvaa, CL Salesa
74 b-continuity and the lexicographic product of graphs NA NA CLSR Vargas, L Sampaio
75 LA b-COLORATION DE CERTAINS GRAPHES NA NA N HAISSAM, M LAISSAOUI, A BENDALI BRAHAM
76 ence on Discrete Mathematics, held 8-11 September 2011 at Amrita University, Coimbatore, Tamil Nadu, India. NA NA NCO Hypercubes, A Anuradha, R Balakrishnan
77 b-chromatic index of graphs 2 NA NA CVGC Limaa, NA Martinsa, L Sampaiob, MC Santosa
78 L'EFFET DE L'AJOUT D'UNE CHAÎNE ÉLÉMENTAIRE Á UN GRAPHE SIMPLE SUR LE NOMBRE b-CHROMATIQUE. NA NA S AGUEB, N MENAD, N IKHLEF ESCHOUF
79 ARÊTE LIFTING ET NOMBRE B-CHROMATIQUE NA NA A BETTACHE, L HOUIDECHE, N IKHLEF ESCHOUF
80 L'INDICE b-CHROMATIQUE DE CERTAINS GRAPHES PARTICULIERS NA NA D ABDESLAMI, N ATTAK, N IKHLEF ESCHOUF
81 ÉTUDE DES b-(SOMMET OU ARÊTE)-COLORATIONS DANS LES GRAPHES ET LEURS COMPORTEMENTS VIS À VIS DE CERTAINES OPÉRATIONS NA NA A BENDALI-BRAHAM, M BLIDIA
82 UNIVERZITA PJ ŠAFARIKA V KOŠICIACH NA NA J Katrenic

Citas de Scrapping

# Año #Citas Título Autores Journal Editor
1 84 The b-chromatic number of cubic graphs M Jakovac, S Klavžar - Graphs and Combinatorics, 2010 - Springer
2 60 On the b-chromatic number of regular graphs S Cabello, M Jakovac - Discrete Applied Mathematics, 2011 - Elsevier
3 32 The b-chromatic number and related topics—a survey M Jakovac, I Peterin - Discrete Applied Mathematics, 2018 - Elsevier
4 26 The b-chromatic index of graphs VA Campos, CV Lima, NA Martins, L Sampaio… - Discrete …, 2015 - Elsevier
5 30 The b-chromatic number of corona graphs T Nadu - Utilitas Mathematica, 2012 - academia.edu
6 8 Bounded Width Graph Classes in Parameterized Algorithms L Jaffke - 2020 - lars-jaffke.github.io
7 30 On the b-coloring of P4-tidy graphs CIB Velasquez, F Bonomo, I Koch - Discrete Applied Mathematics, 2011 - Elsevier
8 7 b-Coloring Parameterized by Clique-Width L Jaffke, PT Lima, D Lokshtanov - Theory of Computing Systems, 2023 - Springer
9 27 On the b-chromatic number of regular graphs without 4-cycle S Shaebani - Discrete Applied Mathematics, 2012 - Elsevier
10 23 b-coloring of Kneser graphs R Balakrishnan, T Kavaskar - Discrete applied mathematics, 2012 - Elsevier
11 1 More results on the z-chromatic number of graphs A Khaleghi, M Zaker - Discrete Applied Mathematics, 2023 - Elsevier
12 13 The b-chromatic index of direct product of graphs I Koch, I Peterin - Discrete Applied Mathematics, 2015 - Elsevier
13 16 b-coloring of tight graphs F Havet, CL Sales, L Sampaio - Discrete Applied Mathematics, 2012 - Elsevier
14 1 A Comparison of the Grundy and b-Chromatic Number of -Free Graphs Z Masih, M Zaker - Graphs and Combinatorics, 2023 - Springer
15 16 On b-colorings and b-continuity of graphs M Alkhateeb - 2012 - core.ac.uk
16 18 The b-chromatic number of some tree-like graphs ASF da Silva - 2010 - theses.hal.science
17 6 New bounds for the b-chromatic number of vertex deleted graphs RR Del-Vecchio, M Kouider - Discrete Applied Mathematics, 2022 - Elsevier
18 12 Algorithmic aspects of graph colourings heuristics L Sampaio - 2012 - theses.hal.science
19 10 b-Chromatic sum of a graph PC Lisna, MS Sunitha - Discrete Mathematics, Algorithms and …, 2015 - World Scientific
20 8 Maximization coloring problems on graphs with few P4 V Campos, C Linhares-Sales, R Sampaio… - Discrete Applied …, 2014 - Elsevier
21 6 -coloring of Cartesian Product of Trees R Balakrishnan, S Francis Raj, T Kavaskar - 2016 - projecteuclid.org
22 0 Structural Parameterizations of b-Coloring L Jaffke, PT Lima, R Sharma - 34th International Symposium on …, 2023 - drops.dagstuhl.de
23 6 A Note on the b-Chromatic Number of Corona of Graphs PC Lisna, MS Sunitha - Journal of Interconnection Networks, 2015 - World Scientific
24 6 On the b-coloring of tight graphs M Kouider, M Zamime - Journal of Combinatorial Optimization, 2017 - Springer
25 7 The b-chromatic number and f-chromatic vertex number of regular graphs A El Sahili, H Kheddouci, M Kouider… - Discrete Applied …, 2014 - Elsevier
26 6 The b-continuity of graphs with large girth CL Sales, A Silva - Graphs and Combinatorics, 2017 - Springer
27 6 On quasi-monotonous graphs M Kouider - Discrete Applied Mathematics, 2016 - Elsevier
28 6 b-Chromatic Number of Subdivision Edge and Vertex Corona T Pathinahan, MA Arokia, D Bhuvaneswari - International Journal of …, 2014 - ijcoa.com
29 7 b-Coloring graphs with large girth V Campos, VAE de Farias, A Silva - Journal of the Brazilian Computer …, 2012 - Springer
30 5 -Coloring is NP-hard on Co-bipartite Graphs and Polytime Solvable on Tree-Cographs F Bonomo, O Schaudt, M Stein, M Valencia-Pabon - Algorithmica, 2015 - Springer
31 4 The b-chromatic number of Mycielskian of some graphs PC Lisna, MS Sunitha - International Journal of …, 2016 - inderscienceonline.com
32 6 b-Chromatic index of graphs CVGC Lima, NA Martins, L Sampaio, MC Santos… - Electronic Notes in …, 2013 - Elsevier
33 4 On the b-coloring of G− e M Zamime, M Kouider, HA Haddadène - Discrete Applied Mathematics, 2015 - Elsevier
34 5 b-coloring of some bipartite graphs. M Blidia, NI Eschouf, F Maffray - Australas. J Comb., 2012 - ajc.maths.uq.edu.au
35 5 A note on approximating the b-chromatic number F Galčík, J Katrenič - Discrete Applied Mathematics, 2013 - Elsevier
36 3 A characterization of edge b-critical graphs A Bendali-Braham, N Ikhlef-Eschouf, M Blidia - Discrete Applied …, 2018 - Elsevier
37 4 On b-vertex and b-edge critical graphs NI Eschouf, M Blidia - Opuscula Mathematica, 2015 - infona.pl
38 0 On the -critical graphs M Zamime - Transactions on Combinatorics, 2024 - toc.ui.ac.ir
39 2 On two conjectures on b-coloring of graph products SF Raj, T Kavaskar - Studia Scientiarum Mathematicarum …, 2017 - akjournals.com
40 2 On the b-Continuity of the Lexicographic Product of Graphs C Linhares Sales, L Sampaio, A Silva - Graphs and Combinatorics, 2017 - Springer
41 3 b-coloring of m-tight graphs CL Sales, L Sampaio - Electronic Notes in Discrete Mathematics, 2009 - Elsevier
42 0 b-Chromatic Sum and b-Continuity Property of Some Graphs PC Lisna, MS Sunitha - Journal of Interconnection Networks, 2021 - World Scientific
43 5 Algorithmes Exacts et Exponentiels pour les Problèmes NP-difficiles sur les Graphes et Hypergraphes C Manfred - 2014 - docnum.univ-lorraine.fr
44 1 Graphs with large girth are b-continuous A Silva, CL Sales - Electronic Notes in Discrete Mathematics, 2016 - Elsevier
45 1 b-chromatic numbers of powers of paths and cycles WH Lin, GJ Chang - Discrete Applied Mathematics, 2013 - Elsevier
46 1 b-continuity and the lexicographic product of graphs CL Sales, R Vargas, L Sampaio - Electronic Notes in Discrete Mathematics, 2015 - Elsevier
47 1 On the Complexity of Subfall Coloring of Graphs D de Andrade, A Silva - Anais do VI Encontro de Teoria da …, 2021 - sol.sbc.org.br
48 0 b-coloring of Central Graph of Triangular Snake N Ansari, RS Chandel, R Jamal - rn - academia.edu
49 3 b-colorações de grafos LS Rocha - 2009 - www-sop.inria.fr
50 0 On the b-Chromatic Sum of Mycielskian of Km, n, Kn and Cn PC Lisna, MS Sunitha - Journal of Interconnection Networks, 2020 - World Scientific
51 0 b-Chromatic Sum of Mycielskian of Paths PC Lisna, MS Sunitha - Electronic Notes in Discrete Mathematics, 2017 - Elsevier
52 0 The lexicographic product of some chordal graphs and of cographs preserves b-continuity CL Sales, L Sampaio, A Silva - Electronic Notes in Discrete Mathematics, 2017 - Elsevier
53 0 On the b-continuity of the lexicographic product of graphs CL Sales, L Sampaio, A Silva - arXiv preprint arXiv:1610.03084, 2016 - arxiv.org
54 0 The b-continuity of graphs with large girth 2 A Silvaa, CL Salesa - arXiv preprint arXiv:1602.01298, 2016 - academia.edu
55 0 A note on approximating the b-chromatic number F Galcıka, J Katrenica - academia.edu
56 0 b-Coloring is NP-Hard on Co-Bipartite Graphs and Polytime Solvable on Tree-Cographs M Valencia-Pabon - … : Third International Symposium, ISCO 2014, Lisbon …, 2014 - Springer
57 0 The workshop on Coverings and Colorings has been organized by DIMA-TIA, KAM and ITI on March 6th, 2009 in the lecture room S9 of School of Computer … PG Gavenciak, P Hell, P Hlinený, P Holub… - kam.mff.cuni.cz
58 1 Tópicos em b-continuidade: Operaçoes em grafos e grafos distância-hereditários LP Magalhães - 2012 - cos.ufrj.br
59 0 HABILITATIONA DIRIGER DES RECHERCHES M VALENCIA-PABON - www-lipn.univ-paris13.fr
60 0 b-coloring of m-tight graphs (Full Version) CLSL Sampaio - Citeseer
61 1 Etude structurelle de quelques classes de graphes M MECHEBBEK - 2013 - pnst.cerist.dz
62 1 b-coloraçao de grafos com poucos P4's V Campos, CL Sales, A Maia, R Sampaio - 2010 - din.uem.br
63 1 Estudo de casos de complexidade de colorações gulosa de vértices e de arestas AKM Oliveira - 2011 - repositorio.ufc.br
64 1 Théorie des graphes, et de l'approximation pour le routage, la coloration et l'apprentissage d'équilibres. J Cohen - PRiSM/CNRS, LIX/école polytechnique - lri.fr
65 0 Uma relaç ao entre b-coloraç ao e teoria espectral em cografos AA Jones, F Protti, RR Del-Vecchio - din.uem.br
66 0 Un enfoque algorítmico sobre algunas variantes del problema de coloreo de grafos y el problema de conjunto independiente máximo IV Koch - 2014 - bibliotecadigital.exactas.uba.ar
67 0 Propriedades espectrais dos grafos P4-esparsos ÁA Jones - 2014 - app.uff.br
68 0 b-coloração e b-continuidade em grafos L Pierezan, MR Cerioli - din.uem.br
69 0 Le nombre b-chromatique de quelques classes de graphes généralisant les arbres M de Werra - 2010 - researchgate.net
70 0 O número b-cromático de alguns gráficos em forma de árvore ASF Silva - 2010 - repositorio.ufc.br
71 9 V Campos, CL Sales, A Maia, R Sampaio - 8th French Combinatorial Conference, 2010
72 0 A Silvaa, CL Salesa - arXiv preprint arXiv:1602.01298, 2016
73 0 N HAISSAM, M LAISSAOUI, A BENDALI BRAHAM - 2022
74 0 CLSR Vargas, L Sampaio
75 0 NCO Hypercubes, A Anuradha, R Balakrishnan
76 0 CVGC Limaa, NA Martinsa, L Sampaiob, MC Santosa…
77 0 S AGUEB, N MENAD, N IKHLEF ESCHOUF - 2020
78 0 A BETTACHE, L HOUIDECHE, N IKHLEF ESCHOUF - 2020
79 0 D ABDESLAMI, N ATTAK, N IKHLEF ESCHOUF - 2018
80 0 Groupes d'automorphismes associés aux colorations de graphes S Kerdjoudj - 2017 - ccdz.cerist.dz
81 0 A BENDALI-BRAHAM, M BLIDIA - 2017
82 0 J Katrenic