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Split-Perfect Graphs: Characterizations and Algorithmic Use
[chapter]
2000
Lecture Notes in Computer Science
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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
2004
SIAM Journal on Discrete Mathematics
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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]
2009
arXiv
pre-print
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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
2011
SIAM Journal on Discrete Mathematics
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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
2021
Asian Review of Mechanical Engineering
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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
2006
Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm - SODA '06
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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]
2015
arXiv
pre-print
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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]
2013
Discrete Mathematics and Its Applications
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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
2006
IEICE transactions on information and systems
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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
2014
Discrete Applied Mathematics
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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]
2015
arXiv
pre-print
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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
1985
Discrete Mathematics
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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
1999
Discrete Applied Mathematics
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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
2007
SIAM Journal on Discrete Mathematics
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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
2012
Journal of Computational Biology
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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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