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Split-Perfect Graphs: Characterizations and Algorithmic Use [chapter]

Andreas Brandstädt, Van Bang Le
2000 Lecture Notes in Computer Science  
This paper characterizes the new class of split-perfect graphs using the concepts of homogeneous sets and p-connected graphs and leads to a linear time recognition algorithm for split-perfect graphs, as  ...  well as efficient algorithms for classical optimization problems on split-perfect graphs based on the primeval decomposition of graphs.  ...  We are grateful to two anonymous referees for their careful reading and helpful comments.  ... 
doi:10.1007/3-540-40064-8_8 fatcat:cffu4ak7yjd37p3ze7qf4p7oxe

Split-Perfect Graphs: Characterizations and Algorithmic Use

Andreas Brandstädt, Van Bang Le
2004 SIAM Journal on Discrete Mathematics  
This paper characterizes the new class of split-perfect graphs using the concepts of homogeneous sets and p-connected graphs and leads to a linear time recognition algorithm for split-perfect graphs, as  ...  well as efficient algorithms for classical optimization problems on split-perfect graphs based on the primeval decomposition of graphs.  ...  We are grateful to two anonymous referees for their careful reading and helpful comments.  ... 
doi:10.1137/s0895480100367676 fatcat:vs55zthq4bddncg2cgm4uknq2y

Generalizing the Splits Equivalence Theorem and Four Gamete Condition: Perfect Phylogeny on Three State Characters [article]

Fumei Lam, Dan Gusfield, Srinath Sridhar
2009 arXiv   pre-print
The resulting incompatibility structure is a hypergraph, which can be used to solve algorithmic and theoretical problems.  ...  We study the perfect phylogeny problem and establish a generalization of the four gamete condition (also called the Splits Equivalence Theorem) for sequences over three state characters.  ...  Schwartz, and T. Warnow for stimulating discussions and suggestions. This research was partially supported by NSF grants SEI-BIO 0513910, CCF-0515378, and IIS-0803564.  ... 
arXiv:0905.1417v2 fatcat:ujyl7xdub5bene7wqgkk5ufyte

Generalizing the Splits Equivalence Theorem and Four Gamete Condition: Perfect Phylogeny on Three-State Characters

Fumei Lam, Dan Gusfield, Srinath Sridhar
2011 SIAM Journal on Discrete Mathematics  
In establishing these results, we prove fundamental structural features of the perfect phylogeny problem on three state characters and completely characterize the obstruction sets that must occur in input  ...  We study the three state perfect phylogeny problem and show that there is a three state perfect phylogeny for a set of input sequences if and only if there is a perfect phylogeny for every subset of three  ...  Schwartz, and T. Warnow for stimulating discussions and suggestions. This research was partially supported by NSF grants SEI-BIO 0513910, CCF-0515378, and IIS-0803564.  ... 
doi:10.1137/090776305 fatcat:oftf7i2kbnd4pp2pkidnpa7qxa

Automatic Detection and Characterization of Weld Defects Using CNN Algorithm in Machine Learning

S. Ramesh Krishnan
2021 Asian Review of Mechanical Engineering  
A dataset created from radiography test data is used for training the algorithm and for writing a program to train this dataset which can be used for defect detection and its characterization.  ...  Convolutional Neural Network (CNN) algorithm in machine learning can be used for the automation of defect detection in radiography thereby reducing human intervention and associated delays.  ...  To view the output in a perceivable manner, matplotlib is used to plot graphs with parameters of the previous step. Two Graphs are generated, model accuracy plot and model loss plot.  ... 
doi:10.51983/arme-2021.10.1.2937 fatcat:guxkbwqjezdedogev5bsvj4n7y

Subgraph characterization of red/blue-split graph and kőnig egerváry graphs

Ephraim Korach, Thành Nguyen, Britta Peis
2006 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm - SODA '06  
We show that KEGs are a special case of a more general class of graph: Red/Blue-split graphs, and give an excluded subgraph characterization of Red/Blue-split graphs.  ...  Kőnig-Egerváry graphs (KEGs) are the graphs whose maximum size of a matching is equal to the minimum size of a vertex cover. We give an excluded subgraph characterization of KEGs.  ...  Acknowledgement: We thank László Lovász, András Frank, Goetz Pfeiffer and Tamás Fleiner for fruitful conversations. We are grateful toÉva Tardos for her help on writing the paper.  ... 
doi:10.1145/1109557.1109650 fatcat:2i3477huofds3o7n75ecwqwrqu

Split Graphs and Nordhaus-Gaddum Graphs [article]

Christine Cheng and Karen L. Collins and Ann Trenk
2015 arXiv   pre-print
We construct bijections between classes of NG-graphs and balanced and unbalanced split graphs which, together with the known formula for the number of split graphs on n vertices, allows us to compute the  ...  A graph G is an NG-graph if \chi(G) + \chi(G complement) = |V(G)| + 1. We characterize NG-graphs solely from degree sequences leading to a linear-time recognition algorithm.  ...  Split graphs are a well-known class of perfect graphs, and thus χ(G) = ω(G) for split graphs. Split graphs also have elegant characterization theorems.  ... 
arXiv:1506.03746v1 fatcat:xpgph22jfjbeffv4nrhvrx2spe

Tolerance Graphs [chapter]

Martin Golumbic
2013 Discrete Mathematics and Its Applications  
Characterize the neighborhood subtree intersection graphs and the neighborhood subtree containment graphs.  ...  Chapters 11 and 12: A recognition algorithm for threshold tolerance (TT) graphs is given in [MRT88] , and we have seen in Chapters 11 and 12 that the graphs P 4 , C 4 , and S 3 are threshold tolerance  ... 
doi:10.1201/b16132-66 fatcat:j2i3oyr2e5au7mtjsdmhmcaezm

Generating Chordal Graphs Included in Given Graphs

M. KIYOMI
2006 IEICE transactions on information and systems  
The class of chordal graphs contains many famous graph classes such as trees, interval graphs, and split graphs, and is also a subclass of perfect graphs.  ...  All our algorithms are based on reverse search method, and time complexities to generate a chordal graph are O(1), and also O(1) delay.  ...  We can characterize chordal graphs by perfect elimination orderings; a graph is chordal if and only if it has a perfect elimination ordering.  ... 
doi:10.1093/ietisy/e89-d.2.763 fatcat:vcqo6fnroje4pdqzvd464qoopi

On opposition graphs, coalition graphs, and bipartite permutation graphs

Van Bang Le
2014 Discrete Applied Mathematics  
Opposition and coalition graphs have been introduced and investigated in connection to perfect graphs.  ...  Recognizing and characterizing opposition and coalition graphs still remain long-standing open problems.  ...  The author thanks the unknown referees for their many helpful comments and suggestions that led to improvements in the presentation of the paper.  ... 
doi:10.1016/j.dam.2012.11.020 fatcat:rqx4xkkmgjhsto5g2jl3ckmt5u

Parameterized Algorithms on Perfect Graphs for deletion to (r,ℓ)-graphs [article]

Sudeshna Kolay and Fahad Panolan and Venkatesh Raman and Saket Saurabh
2015 arXiv   pre-print
I.e. there is an f(r+ℓ) · n^(1) algorithm on perfect graphs on n vertices where f is some (exponential) function of r and ℓ.  ...  It is also known to be fixed-parameter tractable (FPT) on perfect graphs when parameterized by r and ℓ.  ...  Thus, the class of perfect (r, ℓ)-graphs also has a finite forbidden characterization.  ... 
arXiv:1512.04200v1 fatcat:itrvcbkukveqbiz4r2tiarpz7u

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.  ...  We give polynominal-time algorithms to determined whether a general graph is decomposable with respect to the 2-amalgam or 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

Graph classes between parity and distance-hereditary graphs

Serafino Cicerone, Gabriele Di Stefano
1999 Discrete Applied Mathematics  
To this purpose we characterize these classes using Cunningham decomposition and then use the devised structural characterization in order to show efficient algorithms for the recognition and isomorphism  ...  Moreover, the metric characterizations of these two graph classes suggest an excessive gap between them.  ...  Split decomposition has been used to characterize distance-hereditary, circle, and circular-arc graphs, giving efficient algorithms for the recognition [18, 27, 22] and the isomorphism [3, 22] problems  ... 
doi:10.1016/s0166-218x(99)00075-x fatcat:c3k4ab62tzbsfoe7hw7nk7lksa

Recognizing Chordal Probe Graphs and Cycle-Bicolorable Graphs

Anne Berry, Martin Charles Golumbic, Marina Lipshteyn
2007 SIAM Journal on Discrete Mathematics  
Ntriangulatable graphs have properties similar to chordal graphs, and we characterize them using graph separators and using a vertex elimination ordering.  ...  We give several characterizations of chordal probe graphs, first, in the case of a fixed given partition of the vertices into probes and non-probes, and second, in the more general case where no partition  ...  The authors thank the anonymous referee who pointed out an improvement in the complexity of computing the C-components of a graph.  ... 
doi:10.1137/050637091 fatcat:uloxfj7uxrff5ff7ucb6o7ckoa

Comparing Pedigree Graphs

Bonnie Kirkpatrick, Yakir Reshef, Hilary Finucane, Haitao Jiang, Binhai Zhu, Richard M. Karp
2012 Journal of Computational Biology  
We then introduce an algorithm that generates the pedigree graph from this list of descendants.  ...  Our new characterization of a pedigree allows us to introduce a fast heuristic for the edit distance between pedigrees.  ...  Many thanks go to Yun Song for stimulating discussions and to Eran Halperin for the random pedigree simulation.  ... 
doi:10.1089/cmb.2011.0254 pmid:22897201 fatcat:nokklnue3re6hjnc2ppf3chvse
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