Graph cycles and diagram commutativity
Diagrammes, Volume S67-68 (2012), pp. 177-237.
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     author = {Kainen, Paul C.},
     title = {Graph cycles and diagram commutativity},
     journal = {Diagrammes},
     pages = {177--237},
     publisher = {Universit\'e Paris 7, Unit\'e d'enseignement et de recherche de math\'ematiques},
     volume = {S67-68},
     year = {2012},
     mrnumber = {3024906},
     zbl = {1338.05135},
     language = {en},
     url = {http://www.numdam.org/item/DIA_2012__S67-68__177_0/}
}
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Kainen, Paul C. Graph cycles and diagram commutativity. Diagrammes, Volume S67-68 (2012), pp. 177-237. http://www.numdam.org/item/DIA_2012__S67-68__177_0/

[1] Bernhart, F. R. &Amp; Kainen, P. C., On the book thickness of a graph, J. Comb. Th., Ser. B, 27 (1979) no. 3, 320-331. | MR | Zbl

[2] C. H. Bennett, Logical reversibility of computation, IBM J. Res. November 1973, 525-532. | MR | Zbl

[3] R. Brown, From groups to groupoids: A brief survey, Bull. London Math. Soc. 19 (1987) 113-134 | Zbl

[4] D. Deutsch, Quantum theory, the Church-Turing principle and the universal quantum computer, Proc. Royal Soc. of London A 400 (1985) 97-117. | Zbl

[5] Ehresmann, C., Oeuvres Completes, Univ.-de-Picardie, 2000 (4 volumes).

[6] Ehresmann, A. C., Vanbremeersch, J.-P., Memory evolutive systems: hierarchy, emergence, cognition. Elsevier, Amsterdam, 2007. | Zbl

[7] Erdös, P., Fajtlowicz, S., Hoffman, A. J., Maximum degree in graphsof diameter 2Networks 10 (1980) 87-90. | Zbl

[8] Georgakopoulos, A., And Sprüssel, P.Geodesic topological cycles in locally finite graphs. | Zbl

[9] Golubitsky, M., Stewart, I., Nonlinear dynamics of networks: The groupoid formalism, Bull. AMS 43(3) (2006) 305-364. | Zbl

[10] Harary, F., Graph Theory, Addison-Wesley, Reading, MA, 1970. | Zbl

[11] Hechler, S. H., Kainen, P. C., Immersion of digraphs in cubes, Israel J. Math. 18 (1974) 221-233. | Zbl

[12] Kainen, P. C.Some recent results in topological graph theory, in Graphs and combinatorics (Proc. GWU Conf., 1973), Bari, R. A. Harary, F., Eds., Springer Lecture Notes in Math. 406, Berlin, 1974, pp. 76-108. | Zbl

[13] Kainen, P. C., Mathematical cognition, J. of Evolution and Cognition, 4 (1998) 81-89.

[14] Kainen, P. C., On robust cycle bases, in Proc. of 9th Quadrennial Conference on Graph Theory, Combinatorics, Algorithms and Applications, Ed. by Y. Alavi, D. Jones, D. R. Lick, and J. Liu, Kalamazoo, MI, 4?9 June, 2000; Electronic Notes in Discrete Math. 11 art. no. 38, 1-8. | Zbl

[15] Kainen, P. C., Cahiers de topologie et géometrie différentielle catégoriques XLIII (2002) 13-20.

[16] Kainen, P. C., On the Ehresmann-Vanbremeersch theory and mathematical biology, Axiomathes (2009) 19:225-244.

[17] Klemm, K., Stadler, P. F., A note on fundamental, non-fundamental, and robust cycle bases, Discr. Appl. Math. 157 (2009) 2432-2438. | Zbl

[18] Lawvere, F. W., Schanuel, S. H., Introduction to Categories in Continuum Physics, Springer LNM 1174, 1986, pp. 1-16. | Zbl

[19] Lovasz, L.Problem 11, Combinatorial Structures and their Applications, Gorden and Breach (1970).

[20] Mac Lane, S., Categories for the Working Mathematician, Springer. | Zbl

[21] Mitchell, B., Category Theory, Academic Press, NY, 1967.

[22] Moon, J. W., Topics on Tournaments, Holt, Rinehard and Winston, NY, 1968. | Zbl

[23] Online Encyclopedia of Integer Sequences, http:

[24] Ostermeier, P.-J., Et Al., A note on quasi-robust cycle bases, Ars. Math. Contemp. 2 (2009) 231-240. | Zbl

[25] Reshnikov And Turaev?, Ribbon categories?, AMS, 2005?

[26] Shields, I., Shields, B. J., Savage, C. D., An update on the middle levels problem, 309 (2009) 5271-5277. | Zbl

[27] Spanier, E. H., Algebraic topology, McGraw-Hill, NY, 1966. | Zbl

[28] Stewart, I., Golubitsky, M., And Pivato, M., Symmetry groupoids and patterns of synchrony in coupled cell networks, SIAM J. Appl. Dyn. Syst., 2:4 (2003) 609-646. | Zbl

[29] Toffoli, T., Reversible computing, MIT/LCS/TM-151, preprint from http://publications.csail.mit.edu/lcs/pubs/pdf/MIT-LCS-TM-151.pdf | Zbl

[30] Weinstein, A., Groupoids: Unifying internal and external symmetry, Notices A.M.S. 43:7 (1996) 744-752. | Zbl