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The ubiquitous Petersen graph

Gary Chartrand, Héctor Hevia, Robin J. Wilson
1992 Discrete Mathematics  
Wilson, The ubiquitous Petersen graph, Discrete Mathematics 100 (1992) 303-311.  ...  Introduction The Petersen graph is named after the Danish mathematician Julius Petersen (1839 Petersen ( -1910 .  ...  Theorem 1 . 1 The Petersen graph is the only 5-cage.  ... 
doi:10.1016/0012-365x(92)90649-z fatcat:j3ehmu27nndfbe5t5tj5gaku5m

Author index to volume 100 (1992)

1992 Discrete Mathematics  
Wilson, The ubiquitous Petersen graph (l-3) 303-311 Christiansen, M., J. LiItzen, G. Sabidussi and B.  ...  on invariants and the factorisation of graphs 1889  ... 
doi:10.1016/0012-365x(92)90651-u fatcat:3evnx7io6vfnnkthhepx6f3l2q

Page 4160 of Mathematical Reviews Vol. , Issue 93h [page]

1993 Mathematical Reviews  
Gibbons (NZ-AUCK-C) 93h:05162 05C99 05-03 Chartrand, Gary (1-WMI); Hevia, Héctor (1-WMI); Wilson, Robin J. (4-OPEN) The ubiquitous Petersen graph.  ...  This paper gives a selection of problems in which the Petersen graph shows up. The authors have shown  ... 

Page 1402 of Mathematical Reviews Vol. , Issue 86d [page]

1986 Mathematical Reviews  
Graphs and applications (Boulder, Colo., 1982), 69-100, Wiley-Intersci. Publ., Wiley, New York, 1985. If there is a ubiquitous graph in the graph theory literature, it is surely the Petersen graph.  ...  Addi- tional information about the system and its use can be obtained from the authors.” Norman Biggs (Egham) Chartrand, Gary (1-WMI); 86d:05 106 Wilson, Robin J. (4-OX) The Petersen graph.  ... 

The chromatic polynomials of signed Petersen graphs

Matthias Beck, Erika Meza, Bryan Nevarez, Alana Shine, Michael Young
2015 Involve. A Journal of Mathematics  
We developed and executed a computer program (running in SAGE) that efficiently determines the number of proper k-colorings for a given signed graph; our computations for the signed Petersen graphs confirm  ...  Zaslavsky proved in 2012 that, up to switching isomorphism, there are six different signed Petersen graphs and that they could be told apart by their chromatic polynomials, by showing that the latter give  ...  This research was partially supported by the NSF through the grants DMS-1162638 (Beck), DMS-0946431 (Young), and DMS-1156499 (MSRI-UP REU), and by the NSA through grant H98230-11-1-0213.  ... 
doi:10.2140/involve.2015.8.825 fatcat:rojesxuphzeiznsmj6ztwi27xy

Variations on the Petersen Colouring Conjecture

François Pirot, Jean-Sébastien Sereni, Riste Škrekovski
2020 Electronic Journal of Combinatorics  
This bound is tight and the Petersen graph is the only connected graph for which the bound cannot be decreased.  ...  The Petersen colouring conjecture states that every bridgeless cubic graph admits an edge-colouring with 5 colours such that for every edge e, the set of colours assigned to the edges adjacent to e has  ...  then restricting to such a 2-factor required an extra argument to show that the Petersen graph is the only graph for which the bound cannot be improved.  ... 
doi:10.37236/8515 fatcat:dyr2kjwzbnagbfcxn35qo7ffva

Variations on the Petersen colouring conjecture [article]

François Pirot and Jean-Sébastien Sereni and Riste Škrekovski
2019 arXiv   pre-print
This bound is tight and the Petersen graph is the only connected graph for which the bound cannot be decreased.  ...  The Petersen colouring conjecture states that every bridgeless cubic graph admits an edge-colouring with $5$ colours such that for every edge $e$, the set of colours assigned to the edges adjacent to $  ...  Every cubic bridgeless graph admits a normal 5-edge-colouring. Now it is maybe a good time to explain the links with the ubiquitous Petersen graph P.  ... 
arXiv:1905.07913v1 fatcat:c2h6up2e2rcptgrmtmdovq54hi

On Two Unsolved Problems Concerning Matching Covered Graphs [article]

Cláudio L. Lucchesi, Marcelo H. de Carvalho, Nishad Kothari, U. S. R. Murty
2017 arXiv   pre-print
We do this by establishing that a simple nonplanar brick, other than the Petersen graph, is solid if and only if it is C_6-free.  ...  A basic result due to Lovász (1983) states that every nonbipartite matching covered graph is either K_4-based or is C_6-based or both, where C_6 is the triangular prism.  ...  (as they resemble, in our imagination, the two-cornered and three-cornered hats worn by pirates), and the ubiquitous Petersen graph which we denote by P.  ... 
arXiv:1705.09428v1 fatcat:i65ss2p6uzf4nerntvbojedsau

Hamiltonian Paths in Non-Hamiltonian Graphs [article]

Erik Carlson, Willem Fletcher, MurphyKate Montee
2021 arXiv   pre-print
A graph G with n vertices is Hamiltonian if it admits an embedded cycle containing all vertices of G. In any Hamiltonian graph, each vertex is the starting point of a Hamiltonian path.  ...  In this paper we explore the converse. We show that for 29. We then investigate the number of pairs of vertices in a non-Hamiltonian graph G which can be connected by Hamiltonian paths.  ...  One reason the Peterson graph is so ubiquitous in graph theory is its symmetry. In particular, for any pair of edges e, e0 , there is an automorphism of the Petersen graph which sends e to e0 .  ... 
arXiv:2106.13372v1 fatcat:kphohuf2trgvnfy3jyarb6id6u

Measures of Edge-Uncolorability of Cubic Graphs

M. A. Fiol, G. Mazzuoccolo, E. Steffen
2018 Electronic Journal of Combinatorics  
There are many hard conjectures in graph theory, like Tutte's 5-flow conjecture, and the $5$-cycle double cover conjecture, which would be true in general if they would be true for cubic graphs.  ...  The paper closes with a list of open problems and conjectures.  ...  Research supported by the the Catalan Research Council under project 2014SGR1147.  ... 
doi:10.37236/6848 fatcat:gp6i46upuzaonfaw3qxfrrg7zm

High performance networked computing in media, services and information management

Gang Kou
2013 Journal of Supercomputing  
We do appreciate having had the opportunity to supervise the reviewing process of the submissions.  ...  Arabnia, the Editor-in-Chief of The Journal of Supercomputing, for giving us the chance to edit this special issue.  ...  The 3D Petersen-torus network is better than the hypercube-like and star graph-like networks in terms of extendibility.  ... 
doi:10.1007/s11227-013-0942-7 fatcat:ziz3qcncvbfo5nf6lzho4upyse

On measures of edge-uncolorability of cubic graphs: A brief survey and some new results [article]

M.A. Fiol, G. Mazzuoccolo, E. Steffen
2017 arXiv   pre-print
There are many hard conjectures in graph theory, like Tutte's 5-flow conjecture, and the 5-cycle double cover conjecture, which would be true in general if they would be true for cubic graphs.  ...  The paper closes with a list of open problems and conjectures.  ...  Acknowledgements Research supported by the Ministerio de Ciencia e Innovación, Spain, and the European Regional Development Fund under project MTM2014-60127-P, and the Catalan Research Council under project  ... 
arXiv:1702.07156v1 fatcat:56e6ysreure75gupsvey2nuu5m

Page 1732 of Mathematical Reviews Vol. , Issue 87d [page]

1987 Mathematical Reviews  
Many known graphs and classes of graphs are shown to be covered by these construc- tions, among them the ubiquitous Petersen graph and the special S(p+1, 2p) graphs obtained by H. J. Lee {[J. Combin.  ...  It is shown that these graphs are precisely the graphs with Dilworth number at most two (the Dilworth number is the maximum number of pairwise incomparable vertices in the vicinal preorder).  ... 

CONSORTS: A Multiagent Architecture for Content Managements in Ubiquitous Computing
?????????????????????????????????????????CONSORTS

Akio Sashima, Noriaki Izumi, Koichi Kurumatani, Hideyuki Nakashima
2004 Transactions of the Japanese society for artificial intelligence  
In order to extend application areas of the agents from the Internet to the real world, we propose CONSORTS, a multiagent architecture for content managements in ubiquitous computing.  ...  In this paper, we, first, describe two important concepts in order to realize the agent-based content managements in ubiquitous computing, "physically grounding" and "cognitive resources managements."  ...  I., Gold, R., Petersen, K., Goldberg, D., Ellis, J.  ... 
doi:10.1527/tjsai.19.322 fatcat:42tw3ab6w5d3dmdquid7ivtjhq

Hexameric GFP and mCherry Reporters for theDrosophilaGAL4, Q, and LexA Transcription Systems

Harold K. Shearin, Ian S. Macdonald, Laura P. Spector, R. Steven Stowers
2014 Genetics  
the cytoplasm of neurons, including the fine processes of axons and dendrites.  ...  This approach, however, is often limited by the brightness of the fluorescent reporter.  ...  Petersen and Stowers 2011; Shearin et al. 2013) .  ... 
doi:10.1534/genetics.113.161141 pmid:24451596 pmcid:PMC3982691 fatcat:mxj6u74l2jc2hf4h4etgzhepki
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