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Compositions for perfect graphs

G. Cornuéjols, W.H. Cunningham
1985 Discrete Mathematics  
In this paper we introduce a new graph composition, called 2-amalgam, and we prove that the 2-amalgam of perfect graphs is perfect.  ...  This composition generalizes many of the operations known to preserve perfection, such as the clique identification, substitution, join and amalgam operations.  ...  Acknowledgment We are grateful to Bob Bixby and L&z10 Lovasz for pointing out and correcting an error in the original proof of Theorem 1.  ... 
doi:10.1016/s0012-365x(85)80001-7 fatcat:okot6r22zreztb6guaugem7wse

Premises on fuzzy factorizable perfect intrinsic edge-magic graphs

Kaliraja M., Sasikala M.
2019 Malaya Journal of Matematik  
A fuzzy graph G is said to be perfect intrinsic edge-magic if it satisfies the perfect intrinsic edge-magic labelling with intrinsic super constant I s .  ...  In this paper we introduced the order, size and strength of factorizable perfect intrinsic edge-magic graphs. Also we examined these concepts in fuzzy cycle, banner, path & star graphs.  ...  In the above graph, it has Composite order and composite size. Fuzzy factorizable perfect intrinsic edge-magic graphs Definition 3.4. Let G be a FPIEM graph.  ... 
doi:10.26637/mjm0704/0022 fatcat:7pf5kuumhfdtpcn4iimzx44zyu

On Characterizations for Subclasses of Directed Co-Graphs [article]

Frank Gurski, Dominique Komander, Carolin Rehs
2020 arXiv   pre-print
We consider directed and oriented versions of threshold graphs, simple co-graphs, co-simple co-graphs, trivially perfect graphs, co-trivially perfect graphs, weakly quasi threshold graphs and co-weakly  ...  Directed co-graphs are precisely those digraphs which can be defined from the single vertex graph by applying the disjoint union, order composition, and series composition.  ...  (ii) If G 1 and G 2 are directed trivially perfect graphs, then G 1 ⊕ G 2 is a directed trivially perfect graph. 6 Note that the series composition in this case corresponds to the order composition in  ... 
arXiv:1907.00801v2 fatcat:2d755okkgbfyhet6rki4adqw74

On hereditary properties of composition graphs

Vadim E. Levit, E. Mandrescu
1998 Discussiones Mathematicae Graph Theory  
For instance, it is known that the composition graph of a family of perfect graphs is also a perfect graph (B.  ...  In this paper we show that the composition graph of a family of co-graphs (i.e., P 4 -free graphs), is also a co-graph, whereas for θ 1 -perfect graphs (i.e., P 4 -free and C 4 -free graphs) and for threshold  ...  On Hereditary Properties of Composition Graphs  ... 
doi:10.7151/dmgt.1074 fatcat:bkqcmadf7fb6vgn7b6seeis3dy

A perfect matching algorithm for sparse bipartite graphs

Eugeniusz Toczyłowski
1984 Discrete Applied Mathematics  
This paper considers an algorithm for finding a perfect matching, if there is one, in a bipartite graph G.  ...  It is shown that the search for a perfect matching in G may be carried on separately in the strongly connected components of appropriate directed graphs.  ...  Acknowledgments The author is grateful to the anonymous referee for suggestions which helped to refine the paper.  ... 
doi:10.1016/0166-218x(84)90026-x fatcat:sql7c7q7vnfmpmz2jhclp6cnle

Bichromatic P4-composition schemes for perfect orderability

R.B. Hayward, W.J. Lenhart
2004 Discrete Applied Mathematics  
, for example { • • ••; • • ••; • • ••; • • ••}, (3) add edges between the graphs so that in the composed graph each P4 is coloured with an allowable sequence.  ...  A bichromatic P4 composition scheme is as follows: (1) start with two graphs with vertex sets of di erent colour, say black • and white •, (2) select a set of allowable four-vertex bichromatic sequences  ...  Acknowledgements We thank Frà edà eric Ma ray and Irena Rusu for bringing some references to our attention and the referees for helpful comments.  ... 
doi:10.1016/s0166-218x(03)00367-6 fatcat:q7rxntjqrzbgrdroianigp6nbu

Minimum Weighted Clique Cover on Strip-Composed Perfect Graphs [chapter]

Flavia Bonomo, Gianpaolo Oriolo, Claudia Snels
2012 Lecture Notes in Computer Science  
More recently, Chudnovsky and Seymour [3] introduced a composition operation, strip-composition, in order to define their structural results for claw-free graphs; however, this composition operation is  ...  We also design a new, more efficient, combinatorial algorithm for the mwcc problem on strip-composed claw-free perfect graphs.  ...  Let G be a perfect graph, composition of strips H i = (G i , A i ) i = 1, . . . , k w.r.t. a partition P.  ... 
doi:10.1007/978-3-642-34611-8_6 fatcat:bhtkybrokvbsvb2fkiw7qk55qy

Decomposition of perfect graphs

Wen-Lian Hsu
1987 Journal of combinatorial theory. Series B (Print)  
The generalized composition and decomposition operations for Case (a) are perfection preserving. Proof For the composition operation, suppose the composed graph G is not perfect.  ...  We describe composition and decomposition schemes for perfect graphs, which generalize all recent results in this area, e.g., the amalgam and the 2-amalgam split.  ...  APPENDIX: ((-4 N,(u) GCUI G\u 2; G x&4 X0G.V a graph, the vertex set of the graph G, the edge set of the graph G, the complementary graph of G, the size of a largest independent set in G, the size of  ... 
doi:10.1016/0095-8956(87)90031-1 fatcat:mnzneheegbh6xdo2v3qtfz3awy

2 -clique-bond of stable set polyhedra

Anna Galluccio, Claudio Gentile, Paolo Ventura
2013 Discrete Applied Mathematics  
We show how to apply the 2-clique-bond composition to provide the complete linear description of large classes of graphs.  ...  We consider a graph G obtained as the 2-clique-bond of two graphs G 1 and G 2 and we study the polyhedral properties of the stable set polytope associated with this graph.  ...  In addition to those listed above, a number of graph compositions were introduced in the attempt to solve the Strong Perfect Graph Conjecture (now Perfect Graph Theorem [9] ): clique substitution [3]  ... 
doi:10.1016/j.dam.2013.02.022 fatcat:asiiqsjgv5hh3m6z6ypligan6q

Matching and symmetry of graphs

Haruo Hosoya
1986 Computers and Mathematics with Applications  
This paper demonstrates the mathematically beautiful but somewhat mystic relation between the symmetry of a graph and the factorable nature of its perfect matching number.  ...  .), computing the perfect and imperfect matching numbers is commonly performed but under different names, such as partition function for dimer statistics, Kekul6 structures of molecules, paving domino  ...  A part of this work was supported by the Joint Studies Program (1984) of the Institute for Molecular Science.  ... 
doi:10.1016/0898-1221(86)90154-9 fatcat:on4rzre5grfdlb6ib7c5cbxq5m

A note on strong and co-strong perfectness of the X-join of graphs

Alina Szelecka, Andrzej Włoch
1996 Discussiones Mathematicae Graph Theory  
In this paper we discuss strong perfectness and costrong perfectness for the generalized composition (the lexicographic product) of graphs named as the X-join of graphs.  ...  In [4], [3] the following was studied: the problem of strong perfectness for the Cartesian product, the tensor product, the symmetrical difference of n, n ≥ 2, graphs and for the generalized Cartesian  ...  Corollary 1 . 1 The composition X[Y ] of graphs X and Y is strongly perfect if and only if both X and Y are strongly perfect. Using Lemma 4 and Theorem 1 we obtain Corollary 2.  ... 
doi:10.7151/dmgt.1030 fatcat:qp7zhmdlengnrdyo47t63toqgq

On the closure of graphs under substitution

Vassilis Giakoumakis
1997 Discrete Mathematics  
We then give a sufficient condition for ~* to be finite and a simple algorithm for enumerating all the graphs of ~.* As application, we obtain new classes of perfect graphs.  ...  In this paper we investigate the closure ~-* under substitution-composition of a family of graphs ~" defined by a set Lr of forbidden configurations.  ...  Hence, since Lovasz established in [14] that the family of perfect graphs is closed under substitution-composition, each ~* will be a class of perfect graphs.  ... 
doi:10.1016/s0012-365x(96)00358-5 fatcat:ycj7avlix5ew5nkwqwwmw2qm3m

Page 1333 of Mathematical Reviews Vol. , Issue 96c [page]

1996 Mathematical Reviews  
In this paper, we investigate the bandwidth problem for the composition of two graphs and obtain the bandwidth for several classes of graphs of the forms K,[G] and K\,,{G].  ...  This paper explores the relationship between perfect graphs and perfect transversals. A graph G is perfect if for every induced subgraph G’ of G, a(G’) = w(G’).  ... 

On characterizations for subclasses of directed co-graphs

Frank Gurski, Dominique Komander, Carolin Rehs
2020 Journal of combinatorial optimization  
We consider directed and oriented versions of threshold graphs, simple co-graphs, co-simple co-graphs, trivially perfect graphs, co-trivially perfect graphs, weakly quasi threshold graphs and co-weakly  ...  Directed co-graphs are digraphs which can be defined by, starting with the single vertex graph, applying the disjoint union, order composition, and series composition.  ...  In Gurski and Rehs (2018a) we considered digraphs which can be defined by disjoint union, order composition, directed union, and series composition of two directed graphs.  ... 
doi:10.1007/s10878-020-00670-5 fatcat:4t6ezwtrxrdvfmz5ujzw2fo5zm

Perfect edge domination and efficient edge domination in graphs

Chin Lung Lu, Ming-Tat Ko, Chuan Yi Tang
2002 Discrete Applied Mathematics  
Moreover, we present linear-time algorithms to solve the weighted perfect (e cient) edge domination problem on generalized series-parallel graphs and chordal graphs. ?  ...  In this paper, we show that the perfect (e cient) edge domination problem is NP-complete on bipartite (planar bipartite) graphs.  ...  Acknowledgements The authors would like to thank the anonymous referees for many constructive suggestions for the presentation of this paper.  ... 
doi:10.1016/s0166-218x(01)00198-6 fatcat:qsxlnrsivbgzblipnt5scfj6y4
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