Non-hamiltonian graphs in which every edge-contracted subgraph is hamiltonian

Fabrici, Igor; Madaras, Tomáš; Timková, Mária; Cleemput, Nicolas Van; Zamfirescu, Carol T.

doi:10.1016/j.amc.2020.125714

Cited by 4 publications

(11 citation statements)

References 22 publications

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“…To generate networks with desired topology and attributes, the existing SNSs simulate the unobservable (represented with a ) and partially observable network components (represented with a ) based on the observable network components (represented with a ) and an inner rule that directs the network growth (see Table 1). [6], [20], [80], [24], [2], [3], [71], [73], [69], [22], [54], [9], [10], [83], [59], [33], [1], [39], [32], [57], [11], [30], [23], [31] Hybrid [53], [36], [5], [74], [4], [7], [8], [72], [55] [49], [52], [79], [50] [75], [34], [29] [28], [76] [15], [18] As is shown in Table 1, the simulated networks are built with purely simulated topology and attributes, dealing with the unobservability problem of all network components for the analysis of the topological features [1,6,…”

Section: Current State-of-the-art Of Social Network Simulatorsmentioning

confidence: 99%

“…[74], [79], [9], [10], [52], [83], [59], [33], [1], [39], [32], [57], [11], [30], [23], [31] [86], [84], [77], [78], [68], [27] G2a [40], [14] G2b [34], [69], [4], [7], [8], [72], [28], [76], [45], [15], [50] [29], [43], [22], [13] [51], [44] G3 [65] [46], [26], [66] Generation 1 (G1) of models focuses on dynamic process on static networks (see Table 2 and Fig. 1).…”

Section: G1mentioning

confidence: 99%

“…epidemic spreading process on static social networks with a fixed infection rate [27,47]). Most studies focus on SNSs in G1 [1,2,3,5,6,9,10,11, 12, 18,20,23,24,27,30,31,32,33,36,39,49,52,53,54,55,57,59,68,71,73,74,75,77,78,79,80,83,84,86]. Also, many of the simulators generate static social networks without any consideration of dynamic processes [2,3,5,6,18,20,24,36,49,52,…”

Section: G1mentioning

confidence: 99%

“…As is shown in Table 3, most SNSs focus on static networks with no attributes, which G1/G2a [6], [20], [80], [24], [2], [3], [85], [55], [71], [73], [86], [84], [75][77], [78], [31], [40], [27], [68], [21], [1], [9], [83], [59], [33], [39], [10], [32], [57], [11], [30], [23], [53], [36], [5], [74] [18], [54] [49], [52], [79], [70] G2b/G3 [34], [69], [87], [51] [4], [7], [8], [72], [28], [76] [4],…”

Section: G1mentioning

confidence: 99%

See 3 more Smart Citations

Toward Digital Twin Oriented Modeling of Complex Networked Systems and Their Dynamics: A Comprehensive Survey

2022

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This paper aims to provide a comprehensive critical overview on how entities and their interactions in Complex Networked Systems (CNS) are modelled across disciplines as they approach their ultimate goal of creating a Digital Twin (DT) that perfectly matches the reality. We propose four complexity dimensions for the network representation and five generations of models for the dynamics modelling to describe the increasing complexity level of the CNS that will be developed towards achieving DT (e.g. CNS dynamics modelled offline in the 1st generation v.s. CNS dynamics modelled simultaneously with a twoway real time feedback between reality and the CNS in the 5th generation). Based on that, we propose a new framework to conceptually compare diverse existing modelling paradigms from different perspectives and create unified assessment criteria to evaluate their respective capabilities of reaching such an ultimate goal. Using the proposed criteria, we also appraise how far the reviewed current state-of-the-art approaches are from the idealised DTs. Finally, we identify and propose potential directions and ways of building a DT-orientated CNS based on the convergence and integration of CNS and DT utilising a variety of crossdisciplinary techniques.

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Section: Current State-of-the-art Of Social Network Simulatorsmentioning

confidence: 99%

Section: G1mentioning

confidence: 99%

Section: G1mentioning

confidence: 99%

Section: G1mentioning

confidence: 99%

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Toward Digital Twin Oriented Modeling of Complex Networked Systems and Their Dynamics: A Comprehensive Survey

2022

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“…For a survey on hypohamiltonian graphs, see Holton and Sheehan [14]. A subclass of

k

‐graphs in which the exceptional vertices form an independent set is being studied in [12]. Various famous graphs have circumference one less than their order and are thus

k

‐graphs, for example, Petersen's and Coxeter's graph (both

k=0

), Tietze's graph (

k=3

), Grinberg's graph (

k=4

, see Grünbaum [13]), Herschel's graph and the Goldner–Harary graph (both

k=5

, see Corollary 2), Kirkman's graph (

k=6

), the Tutte graph (

k=13

), the Lederberg–Bosák–Barnette graph (

k=14

, see Neyt [20]), Meredith's graph (

k=40

), and many but not all small snarks [7].…”

Section: Introductionmentioning

confidence: 99%

On the hamiltonicity of a planar graph and its vertex‐deleted subgraphs

Zamfirescu

2022

Journal of Graph Theory

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Tutte proved that every planar 4-connected graph is hamiltonian. Thomassen showed that the same conclusion holds for the superclass of planar graphs with minimum degree at least 4 in which all vertex-deleted subgraphs are hamiltonian. We here prove that if in a planar n-vertex graph with minimum degree at least 4 at least n − 5 vertex-deleted subgraphs are hamiltonian, then the graph contains two hamiltonian cycles, but that for every c < 1 there exists a nonhamiltonian polyhedral n-vertex graph with minimum degree at least 4 containing cn hamiltonian vertex-deleted subgraphs. Furthermore, we study the hamiltonicity of planar triangulations and their vertex-deleted subgraphs as well as Bondy's meta-conjecture, and prove that a polyhedral graph with minimum degree at least 4 in which all vertex-deleted subgraphs are traceable, must itself be traceable.

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Review and Assessment of Digital Twin–Oriented Social Network Simulators

Wen,

Gabrys,

Musial

2023

IEEE Access

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The ability to faithfully represent real social networks is critical from the perspective of testing various what-if scenarios which are not feasible to be implemented in a real system as the system's state would be irreversibly changed. High fidelity simulators allow one to investigate the consequences of different actions before introducing them to the real system. For example, in the context of social systems, an accurate social network simulator can be a powerful tool used to guide policy makers, help companies plan their advertising campaigns or authorities to analyse fake news spread. In this study we explore different Social Network Simulators (SNSs) and assess to what extent they are able to mimic the real social networks. We conduct a critical review and assessment of existing Social Network Simulators under the Digital Twin-Oriented Modelling framework proposed in our previous study. We subsequently extend one of the most promising simulators from the evaluated ones, to facilitate generation of social networks of varied structural complexity levels. This extension brings us one step closer to a Digital Twin Oriented SNS (DT Oriented SNS). We also propose an approach to assess the similarity between real and simulated networks with the composite performance indexes based on both global and local structural measures, while taking runtime of the simulator as an indicator of its efficiency. We illustrate various characteristics of the proposed DT Oriented SNS using a well known Karate Club network as an example. While not considered to be of sufficient complexity, the simulator is intended as one of the first steps on a journey towards building a Digital Twin of a social network that perfectly mimics the reality.

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Non-hamiltonian graphs in which every edge-contracted subgraph is hamiltonian

Cited by 4 publications

References 22 publications

Toward Digital Twin Oriented Modeling of Complex Networked Systems and Their Dynamics: A Comprehensive Survey

Toward Digital Twin Oriented Modeling of Complex Networked Systems and Their Dynamics: A Comprehensive Survey

On the hamiltonicity of a planar graph and its vertex‐deleted subgraphs

Review and Assessment of Digital Twin–Oriented Social Network Simulators

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