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Decompositions for the edge colouring of reduced indifference graphs

Celina M.H. de Figueiredo, João Meidanis, Célia Picinin de Mello, Carmen Ortiz
2003 Theoretical Computer Science  
We present two decomposition methods for edge colouring reduced indi erence graphs with maximum degree colours.  ...  The chromatic index problem-ÿnding the minimum number of colours required for colouring the edges of a graph-is still unsolved for indi erence graphs, whose vertices can be linearly ordered so that the  ...  Acknowledgements We thank Marisa Gutierrez for introducing us to the class of minimum indi erence graphs.  ... 
doi:10.1016/s0304-3975(02)00636-9 fatcat:bldj2msqzffdzfzg4ipqlladce

Page 2750 of Mathematical Reviews Vol. , Issue 2004d [page]

2004 Mathematical Reviews  
(BR-FRJ-IM; Rio de Janeiro) ; Meidanis, Joao (BR-ECP-C; Campinas) ; de Mello, Célia Picinin (BR-ECP-C; Campinas); Ortiz, Carmen Decompositions for the edge colouring of reduced indifference graphs.  ...  We present two decomposition methods for edge colouring reduced indifference graphs with maximum degree colours.” 2004d:05068 05C15 Gravier, Sylvain (F-CNRS-LL; Grenoble) ; Maffray, Frédéric (F-CNRS-LL  ... 

Edge-colouring and total-colouring chordless graphs

Raphael C.S. Machado, Celina M.H. de Figueiredo, Nicolas Trotignon
2013 Discrete Mathematics  
The proofs are algorithmic in the sense that we actually output an optimal colouring of a graph instance in polynomial time.  ...  We describe a known decomposition result for chordless graphs and use it to establish that every chordless graph of maximum degree Δ≥ 3 has chromatic index Δ and total chromatic number Δ + 1.  ...  If, for each edge uv ∈ E, |L uv | ≥ max{3, deg G (u), deg G (v)}, then there is an edge-colouring π of G such that, for each edge uv ∈ E, π(uv) ∈ L uv . Proof -Let G be the reduced graph of G.  ... 
doi:10.1016/j.disc.2013.03.020 fatcat:oye6jvujxzg7zc6pjn7h65gfii

Edge Colouring Reduced Indifference Graphs [chapter]

Celina M. H. de Figueiredo, Célia Picinin de Mello, Carmen Ortiz
2000 Lecture Notes in Computer Science  
The chromatic index problem { nding the minimum number of colours required for colouring the edges of a graph { is still unsolved for indi erence graphs, whose vertices can be linearly ordered so that  ...  We prove that every indi erence graph having no twin maximum degree vertices is Class 1. We present two decomposition methods for edge colouring reduced indi erence graphs.  ...  1 colours and one additional colour is needed to colour the edges in the matching M. This implies that G is Class 1. Corollary 2 All reduced indi erence graphs are Class 1.  ... 
doi:10.1007/10719839_16 fatcat:bsf2wk55pbgljl3xpyz7m57mbm

On edge-colouring indifference graphs [chapter]

Celina M. H. Figueiredo, João Meidanis, Célia Picinin Mello
1995 Lecture Notes in Computer Science  
Vizing's theorem states that the chromatic index x'(G) of a graph G is either the maxi- . Plantholt proved that this condition is necessary for graphs with a universal vertex.  ...  In this paper, we conjecture that, for indifference graphs, this is also true.  ...  Szwarcfiter for proposing the problem of edge-colouring indifference graphs to us. We thank Clhdio L. Lucchesi for many interesting discussions on edge-colourings; and also Luiz H.  ... 
doi:10.1007/3-540-59175-3_96 fatcat:bsaef2s2kbc7pphtz34fsfzxki

On edge-colouring indifference graphs

Celina M.H. de Figueiredo, João Meidanis, Célia Picinin de Mello
1997 Theoretical Computer Science  
Vizing's theorem states that the chromatic index x'(G) of a graph G is either the maxi- . Plantholt proved that this condition is necessary for graphs with a universal vertex.  ...  In this paper, we conjecture that, for indifference graphs, this is also true.  ...  Szwarcfiter for proposing the problem of edge-colouring indifference graphs to us. We thank Clhdio L. Lucchesi for many interesting discussions on edge-colourings; and also Luiz H.  ... 
doi:10.1016/s0304-3975(96)00264-2 fatcat:hnebebtllnhl7gqbdb3mqm2hpa

Author index

2003 Theoretical Computer Science  
Ortiz, Decompositions for the edge colouring of reduced indifference graphs (1-3) 145-155 de Mello, C.P., see C.M.H. de Figueiredo (1-3) 145-155 Denise, A., see S.  ...  Molloy, Analysis of edge deletion processes on faulty random regular graphs (1-3) 241-260 Grabner, P.J., A. Knopfmacher and H.  ... 
doi:10.1016/s0304-3975(03)00124-5 fatcat:ixtkkstovvbd3l6njhzwhde2xy

Fast Dynamic Programming on Graph Decompositions [article]

Johan M. M. van Rooij, Hans L. Bodlaender, Erik Jan van Leeuwen, Peter Rossmanith, Martin Vatshelle
2018 arXiv   pre-print
We improve the running time of dynamic programming algorithms on these graph decompositions for a large number of problems as a function of the treewidth, branchwidth, or cliquewidth, respectively.  ...  The main techniques used in this paper are a generalisation of fast subset convolution, as introduced by Björklund et al., now applied in the setting of graph decompositions and augmented such that multiple  ...  The first author also thanks Jesper Nederlof for several useful discussions.  ... 
arXiv:1806.01667v1 fatcat:ru2qt6fg2fanrorhdjosmbvxqq

Total Colourings - A survey [article]

Geetha Jayabalan and Narayanan N and K Somasundaram
2018 arXiv   pre-print
The smallest integer k needed for the assignment of colors to the elements so that the coloring is proper (vertices and edges) is called the total chromatic number of a graph.  ...  Vizing and Behzed conjectured that the total coloring can be done using at most Δ(G)+2 colors, where Δ(G) is the maximum degree of G. It is not settled even for planar graphs.  ...  In the same paper, Sanchez-Arroyo also proved that the problem is NPcomplete even for cubic bipartite graphs. For general classes of graphs, the total coloring would be harder than edge colouring.  ... 
arXiv:1812.05833v1 fatcat:2igatxvf55bcncqp2q2riwpp2y

Comparative analysis of articulated and behavioural social networks in a social news sharing website

Andreas Kaltenbrunner, Gustavo Gonzalez, Ricard Ruiz De Querol, Yana Volkovich
2011 New Review of Hypermedia and Multimedia  
A k-core decomposition of the networks reveals a fundamental difference in the practice of establishing behavioural and articulated links.  ...  The explicit network is given in the form of declared but not necessarily bidirectional friendship links; the behavioural network is extracted from conversations through comments to the shared links.  ...  Acknowledgements The authors wish to thank Vicenç Gó mez and David Laniado for helping in the evaluation of this study and Meneame.net for allowing access to an anonymised dump of their database.  ... 
doi:10.1080/13614568.2011.598192 fatcat:db4de43pdbhypnwm3szj7z6ucq

The Strong Perfect Graph Conjecture: 40 years of attempts, and its resolution

F. Roussel, I. Rusu, H. Thuillier
2009 Discrete Mathematics  
The Strong Perfect Graph Conjecture (SPGC) was certainly one of the most challenging conjectures in graph theory.  ...  Strong Perfect Graph Theorem (SPGT); (2) we briefly present the other "direct" attempts, that is, those for which results exist showing one (possible) way to the proof; (3) we ignore entirely the "indirect  ...  Fouquet for his encouragements and his helpful suggestions regarding the contents of the paper, as well as for his participation in the writing of Section 4.  ... 
doi:10.1016/j.disc.2009.05.024 fatcat:kyvppq6dmndhlfn6j4jszqgvva

Monadic second-order logic and the domino problem on self-similar graphs [article]

Laurent Bartholdi
2020 arXiv   pre-print
This covers, for example, the Sierpi\'nski gasket graphs and the Schreier graphs of the Basilica group.  ...  On the other hand, we already prove undecidability of the domino problem for a class of self-similar groups, answering a question by Barbieri and Sablik, and some examples including one of linear growth  ...  We indifferently use N for the subtransducer or the corresponding subset of G. The minimal such N is called the nucleus of the action.  ... 
arXiv:2011.02735v1 fatcat:vun3sghucve7zglgusdaq65a54

Cycle transversals in bounded degree graphs

Marina Groshaus, Pavol Hell, Sulamita Klein, Loana Tito Nogueira, Fábio Protti
2011 Discrete Mathematics & Theoretical Computer Science  
cycles with k vertices of the input graph, for a fixed k \textgreater= 3.  ...  We also discuss polynomial-time approximation algorithms for computing C(3)-transversals in graphs of maximum degree at most four, based on a new decomposition theorem for such graphs that leads to useful  ...  Acknowledgments The authors are very grateful to the two anonymous referees for providing us with constructive comments and suggestions, which greatly improved the presentation of this work.  ... 
doi:10.46298/dmtcs.533 fatcat:dfpesobfpzbahaft6ee7ebcj3a

Reconstructing the pre-doubling genome

Nadia El-Mabrouk, David Bryant, David Sankoff
1999 Proceedings of the third annual international conference on Computational molecular biology - RECOMB '99  
We present an exact algorithm for reconstructing the ancestral pm-doubling genome in polynomial time, minimizing in key cases the number of translocations required to derive the observed order and orientation  ...  We apply this to the genome duplication which has been described for Saccharomyces cerevisiae.  ...  Each vertex is incident to exactly one black and one gray edge, so that there is a unique decomposition of 812 into cl2 disjoint cycles of alternating edge colours.  ... 
doi:10.1145/299432.299475 dblp:conf/recomb/El-MabroukBS99 fatcat:nc66whfwajbyzlifnhhhx36nuy

Rationalisation of Profiles of Abstract Argumentation Frameworks: Characterisation and Complexity

Stéphane Airiau, Elise Bonzon, Ulle Endriss, Nicolas Maudet, Julien Rossit
2017 The Journal of Artificial Intelligence Research  
., concerning the types of preferences used or the number of distinct values involved.  ...  is induced by a combination of, first, some basic factual attack-relation between the arguments and, second, the personal preferences of the agent concerned regarding the moral or social values the arguments  ...  We are grateful for the feedback received from several anonymous reviewers.  ... 
doi:10.1613/jair.5436 fatcat:6j2lswqmzzb2rp6uzccezch2ha
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