Abstract
We introduce a new framework designed for constructing graphs with given circular chromatic index. This framework allows construction of graphs with arbitrary maximum degree and with additional properties, e.g. high connectivity or large girth. We utilize this framework to construct a cyclically 4-edge-connected cubic graph with girth 5 and circular chromatic index r for any rational r ∈ (3, 3 + 1/4.5).
The authors acknowledge partial support from the research grant APW-0223-10 and from the APW grant ESF-EC-0009-10 within the EUROCORES Programme EUROGIGA (project GRe-GAS) of the European Science Foundation. The second author also acknowledges partial support from the Trnava University grant 8/TU/13.
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References
P. Afshani, M. Ghandehari, M. Ghandehari, H. Hatami, R. Tusserkani and X. Zhu, Circular chromatic index of graphs of maximum degree 3, J. Graph Theory 49 (2005), 325–335.
M. Ghebleh, Circular chromatic index of generalized Blanusa snarks, Electron. J. Combin. 15 (2008).
D. Král’, E. Máčajová, J. Mazák and J.-S. Sereni, Circular edge-colourings of cubic graphs with girth six, J. Combin. Theory Ser.B 100 (2010), 351–358.
R. Lukot’ka and J. Mazák, Cubic graphs with given circular chromatic index, SIAM J. Discrete Math. 24(3) (2011), 1091–1103.
J. Mazák, Circular chromatic index of type 1 Blanuša snarks, J. Graph Theory 59 (2008), 89–96.
R. Nedela and M. Škoviera, Decompositions and reductions of snarks, J. Graph Theory 22 (1996), 253–279.
X. Zhu, Circular chromatic number: a survey, Discrete Math. 29 (2001) 371–410.
X. Zhu, Recent developments in circular colourings of graphs, In: “Topics in Discrete Mathematics”, Springer, 2006, 497–550.
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© 2013 Scuola Normale Superiore Pisa
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Lukot’ka, R., Mazák, J. (2013). Non-trivial snarks with given circular chromatic index. In: Nešetřil, J., Pellegrini, M. (eds) The Seventh European Conference on Combinatorics, Graph Theory and Applications. CRM Series, vol 16. Edizioni della Normale, Pisa. https://doi.org/10.1007/978-88-7642-475-5_11
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DOI: https://doi.org/10.1007/978-88-7642-475-5_11
Publisher Name: Edizioni della Normale, Pisa
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Online ISBN: 978-88-7642-475-5
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