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The graph isomorphism problem on geometric graphs

Ryuhei Uehara
2014 Discrete Mathematics & Theoretical Computer Science  
The properties of these graph classes on the boundary indicate us the essence of difficulty of the GI problem.  ...  In this paper, we survey the computational complexity of the problem on some graph classes that have geometric characterizations.  ...  One of basic problems for graph classes is the recognition problem. That is, for any given graph G and some graph class C, the recognition problem asks if G is a member of C or not.  ... 
doi:10.46298/dmtcs.2076 fatcat:opywyghknffdpgho5jaxuycgwm

New results on generalized graph coloring [article]

Vladimir E. Alekseev, Alastair Farrugia, Vadim V. Lozin
2003 arXiv   pre-print
For graph classes P_1,...,P_k, Generalized Graph Coloring is the problem of deciding whether the vertex set of a given graph G can be partitioned into subsets V_1,...  ...  . = P_k is the class of edgeless graphs, then this problem coincides with the standard vertex k- colorability, which is known to be NP-complete for any k> 3.  ...  As one of the smallest classes in this gap with unknown recognition time complexity, let us point out (P, Q)-colorable graphs with P = O and Q = F ree(2K 2 , P 4 ), where 2K 2 is the disjoint union of  ... 
arXiv:math/0306178v1 fatcat:xuzu6r3dxjbalmpofrnm524kvu

New Results on Generalized Graph Coloring

Vladimir E. Alekseev, Alastair Farrugia, Vadim V. Lozin
2004 Discrete Mathematics & Theoretical Computer Science  
International audience For graph classes \wp_1,...,\wp_k, Generalized Graph Coloring is the problem of deciding whether the vertex set of a given graph G can be partitioned into subsets V_1,...  ...  Recently, this result has been generalized by showing that if all \wp_i's are additive hereditary, then the generalized graph coloring is NP-hard, with the only exception of bipartite graphs.  ...  Acknowledgements The second author wishes to thank R.  ... 
doi:10.46298/dmtcs.311 fatcat:p7d3l73pr5ft7c2hq45p6fdp4m

Small world models for social network algorithms testing

Igor Kanovsky
2010 Procedia Computer Science  
This paper proposes models of networks with these properties and algorithm for community structure recognition.  ...  Social networks have small-world property, hierarchical community structure, and some other properties.  ...  By simulation of some link redirection processes, the models with community structure and small-world properties were generated.  ... 
doi:10.1016/j.procs.2010.04.263 fatcat:yhvveod35vdcfdzg4ganam4s6y

The P versus NP–complete dichotomy of some challenging problems in graph theory

Celina M.H. de Figueiredo
2012 Discrete Applied Mathematics  
Some open problems are discussed: the stubborn problem for list partition, the chromatic index of chordal graphs, and the recognition of split clique graphs.  ...  We shall discuss our contribution through the classification of some long-standing problems in important areas of graph theory: perfect graphs, intersection graphs, and structural characterization of graph  ...  Ferreira and to Fabio Protti, the Program Chairs of LAGOS 2009, for the opportunity of giving this invited talk. Special thanks are due to my co-authors.  ... 
doi:10.1016/j.dam.2010.12.014 fatcat:vou3y5m4izgzpcgze6ocw6llrm

Page 4753 of Mathematical Reviews Vol. , Issue 94h [page]

1994 Mathematical Reviews  
For the properties of being connected, and having exactly k comparable pairs we show that the recognition complexity is (3); the complexity of interval orders is exactly (5) — 1.  ...  ; Berlin); Wagner, Dorothea (D-TUB; Berlin) On the complexity of partial order properties.  ... 

Recognizing Chordal Probe Graphs and Cycle-Bicolorable Graphs

Anne Berry, Martin Charles Golumbic, Marina Lipshteyn
2007 SIAM Journal on Discrete Mathematics  
If no partition is given in advance, the complexity of our recognition algorithm is O(|E| 2 ).  ...  The corresponding recognition complexity for chordal probe graphs, given a partition of the vertices into probes and non-probes, is O(|P ||E|), thus also providing an interesting tractable subcase of the  ...  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

A New Method for Biostatistical miRNA Pattern Recognition with Topological Properties of Visibility Graphs in 3D Space

Matej Babič, Ninoslav Marina, Andrej Mrvar, Kumar Dookhitram, Michele Calì
2019 Journal of Healthcare Engineering  
Statistical methods have been used to calculate the topological properties of a visibility graph in pattern recognition.  ...  Thus, the construction of 3D visibility graphs is highly complex and requires professional computers or supercomputers.  ...  Acknowledgments is research was supported in part by European Union, European Social Fund, and a benefit obtained with the fund for the athenaeum research in Catania, research programme 2019/2021.  ... 
doi:10.1155/2019/4373760 pmid:31281616 pmcid:PMC6594254 fatcat:jy6jaz7vvzdwbi7pvxycdomccm

Assessing Complexity Results in Feature Theories [article]

Marten Trautwein
1995 arXiv   pre-print
On the one hand, the complexity of feature theories does not provide an upper bound for the complexity of such unification grammars.  ...  We show that from these complexity results no immediate conclusions can be drawn about the complexity of the recognition problem of unification grammars using these feature theories.  ...  Hence, even when we confine ourselves to decidable problems, the complexity of the recognition problem of a unification grammar that uses some feature theory may be higher than the complexity of the satisfiability  ... 
arXiv:cmp-lg/9503022v1 fatcat:5xx6mc6jx5hfdh7ok2cqfqijjm

Quantitative Graph Theory: A new branch of graph theory and in network science [article]

Matthias Dehmer, Frank Emmert-Streib, Yongtang Shi
2017 arXiv   pre-print
The main goal of quantitative graph theory is the structural quantification of information contained in complex networks by employing a measurement approach based on numerical invariants and comparisons  ...  We provide examples of how quantitative graph theory can be used for novel applications in the context of the overarching concept network science.  ...  Matthias Dehmer gratefully acknowledges financial support from the German Federal Ministry of Education and Research (BMBF) (project RiKoV, Grant No. 13N12304).  ... 
arXiv:1710.05660v1 fatcat:sdalpy7jmnddbcxwek4gsy346e

Using Description Logics for RDF Constraint Checking and Closed-World Recognition [article]

Peter F. Patel-Schneider
2015 arXiv   pre-print
When the information sources are expressed in well-behaved RDF or RDFS (i.e., RDF graphs interpreted in the RDF or RDFS semantics) this constraint checking and closed-world recognition is simple to describe  ...  RDF and Description Logics work in an open-world setting where absence of information is not information about absence.  ...  New properties are not allowed because they may increase the computational complexity of closed-world recognition.  ... 
arXiv:1411.4156v2 fatcat:od3pvanarravzdqf5v65xxcloe

Faster recognition of clique-Helly and hereditary clique-Helly graphs

Min Chih Lin, Jayme L. Szwarcfiter
2007 Information Processing Letters  
These algorithms also reduce the complexity of recognizing some other classes, as disk-Helly graphs.  ...  The best algorithms currently known to recognize clique-Helly and hereditary clique-Helly graphs have complexities O(nm 2 ) and O(n 2 m), respectively for a graph with n vertices and m edges.  ...  Introduction The Helly property has been studied in many contexts, as in combinatorics and geometry. Within graph theory, the Helly property has been applied to some different families of sets.  ... 
doi:10.1016/j.ipl.2007.02.017 fatcat:437fimvx4rctljtdeh6mtxgbie

Musings on Symbol Recognition [chapter]

Karl Tombre, Salvatore Tabbone, Philippe Dosch
2006 Lecture Notes in Computer Science  
Figure 3 gives some examples of complex symbols from the area of aeronautics (wiring diagrams of an Airbus plane).  ...  Figure 1 : 1 Example of graph organization based on the junction points(from [39] ). Figure 3 : 3 Examples of complex symbols.  ... 
doi:10.1007/11767978_3 fatcat:tdynx36hwrbhtbe2r5omybnogq

Recognizing Bipolarizable and P 4-Simplicial Graphs [chapter]

Stavros D. Nikolopoulos, Leonidas Palios
2003 Lecture Notes in Computer Science  
Moreover, we present a diagram on class inclusions and the currently best recognition time complexities for a number of perfectly orderable classes of graphs and some preliminary results on forbidden subgraphs  ...  In this paper, we consider the recognition problem on these classes of graphs and present algorithms that solve it in O(nm) time, where n and m are the numbers of vertices and of edges of the input graph  ...  We have also presented results on class inclusions and recognition time complexities for a number of perfectly orderable classes of graphs, and also some results on forbidden subgraphs for the class of  ... 
doi:10.1007/978-3-540-39890-5_31 fatcat:z5cp6bh5c5gwpnbrmhehzec3xa

Characterizations and recognition of circular-arc graphs and subclasses: A survey

Min Chih Lin, Jayme L. Szwarcfiter
2009 Discrete Mathematics  
Circular graphs are intersection graphs of arcs on a circle.  ...  In the present paper, we survey these characterizations and recognition algorithms, with emphasis on the linear time algorithms.  ...  Tucker wrote his PhD thesis on this class in 1969 [71] , and in the 1970's published a series of articles [72, 73, [75] [76] [77] containing some fundamental properties on circular-arc graphs and subclasses  ... 
doi:10.1016/j.disc.2008.04.003 fatcat:vtlfg2sruvdrtfmzxa46vteteq
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