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The graph isomorphism problem on geometric graphs

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. ...

##
###
New results on generalized graph coloring
[article]

2003
*
arXiv
*
pre-print

For

arXiv:math/0306178v1
fatcat:xuzu6r3dxjbalmpofrnm524kvu
*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*...##
###
New Results on Generalized Graph Coloring

2004
*
Discrete Mathematics & Theoretical Computer Science
*

International audience For

doi:10.46298/dmtcs.311
fatcat:p7d3l73pr5ft7c2hq45p6fdp4m
*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. ...##
###
Small world models for social network algorithms testing

2010
*
Procedia Computer Science
*

This paper proposes models

doi:10.1016/j.procs.2010.04.263
fatcat:yhvveod35vdcfdzg4ganam4s6y
*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. ...##
###
The P versus NP–complete dichotomy of some challenging problems in graph theory

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. ...

##
###
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

2007
*
SIAM Journal on Discrete Mathematics
*

If no partition is given in advance,

doi:10.1137/050637091
fatcat:uloxfj7uxrff5ff7ucb6o7ckoa
*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*. ...##
###
A New Method for Biostatistical miRNA Pattern Recognition with Topological Properties of Visibility Graphs in 3D Space

2019
*
Journal of Healthcare Engineering
*

Statistical methods have been used to calculate

doi:10.1155/2019/4373760
pmid:31281616
pmcid:PMC6594254
fatcat:jy6jaz7vvzdwbi7pvxycdomccm
*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. ...##
###
Assessing Complexity Results in Feature Theories
[article]

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 ...

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

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). ...

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

2015
*
arXiv
*
pre-print

When

arXiv:1411.4156v2
fatcat:od3pvanarravzdqf5v65xxcloe
*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*. ...##
###
Faster recognition of clique-Helly and hereditary clique-Helly graphs

2007
*
Information Processing Letters
*

These algorithms also reduce

doi:10.1016/j.ipl.2007.02.017
fatcat:437fimvx4rctljtdeh6mtxgbie
*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. ...##
###
Musings on Symbol Recognition
[chapter]

2006
*
Lecture Notes in Computer Science
*

Figure 3 gives

doi:10.1007/11767978_3
fatcat:tdynx36hwrbhtbe2r5omybnogq
*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. http://www.epeires.org/ ...##
###
Recognizing Bipolarizable and P 4-Simplicial Graphs
[chapter]

2003
*
Lecture Notes in Computer Science
*

Moreover, we present a diagram

doi:10.1007/978-3-540-39890-5_31
fatcat:z5cp6bh5c5gwpnbrmhehzec3xa
*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*...##
###
Characterizations and recognition of circular-arc graphs and subclasses: A survey

2009
*
Discrete Mathematics
*

Circular

doi:10.1016/j.disc.2008.04.003
fatcat:vtlfg2sruvdrtfmzxa46vteteq
*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 ...
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