Abstract
The clique covering number of a graph is the smallest number of complete subgraphs needed to cover its edge-set. For each n, we determine the set of those integers which are clique covering numbers of connected, cubic graphs on n vertices. The analogous result for 4-regular graphs is stated.
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References
Bondy, J.A. and Murty, U.S.R., Graph Theory with Applications, The MacMillan Press, London (1977).
Caccetta, L. and Pullman, N.J., "Clique Covering Numbers of Regular Graphs."
Eades, P., Pullman, N.J. and Robinson, P.J., "On Clique Partition Numbers of Regular Graphs", Proceedings of The Waterloo Conference on Combinatorial Mathematics, University of Waterloo, 1982.
Erdős, P., Goodman, A.W., and Pósa, L., "The Representation of a Graph by Set Intersections", Can. J. Math. v.18 (1966), pp.106–112.
Gregory, D.A. and Pullman, N.J., "On a Clique Covering Problem of Orlin", Discrete Mathematics (to appear).
Lovász, L., "On covering of graphs", Theory of Graphs, (Proceedings of the Colloquium held at Tihany, Hungary, September 1966), (P. Erdős and G. Katona eds.) Academic Press, N.Y. (1968)-pp.231–236.
Orlin, J., "Contentment in Graph Theory: Covering Graphs with Cliques", K. Nederlandse Ak. van Wetenschappen Proc. Ser. A,V. 80 (1977), pp.406–424.
Pullman, N.J. and de Caen, D., "Clique Coverings of Graphs I: cliquepartitions of regular graphs", Utilitas Math. v.19 (1981) pp.177–206.
Pullman, N.J. and Donald, A.W., "Clique Coverings of Graphs II: complements of complete graphs", Utilitas Math. V.19 (1981) pp.207–214.
Pullman, N.J. and de Caen, D., "Clique Coverings of Graphs III: cliquecoverings of regular graphs", Congressus Numerantium, V.29 (1980), pp.795–808.
Pullman, N.J., "Clique Coverlings of Graphs IV–Algorithms", (to appear).
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© 1983 Springer-Verlag
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Caccetta, L., Pullman, N.J. (1983). On clique covering numbers of cubic graphs. In: Casse, L.R.A. (eds) Combinatorial Mathematics X. Lecture Notes in Mathematics, vol 1036. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0071513
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DOI: https://doi.org/10.1007/BFb0071513
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