Abstract
In this paper we find upper bounds for the mincut value of Cayley graphs over abelian groups. These results provide a significant improvement of those in Annextein and Baumslag (Math. Syst. Theory 26(3):271–291, [1993]).
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Annexstein, F., Baumslag, M.: On the diameter and bisector size of Cayley graphs. Math. Syst. Theory 26(3), 271–291 (1993)
Assman, S., Peck, G., Syslo, M., Zak, J.: The bandwidth of caterpillars with hairs of length 1 and 2. SIAM J. Algebr. Discrete Methods 2, 387–393 (1981)
Bodlaender, H.L., Serna, M.J., Thilikos, D.M.: A polynomial algorithm for the cutwidth of bounded degree graphs with small treewidth. Technical Report UU-CS-2001-04, Utrecht University, Information and Computing Sciences (2001)
Conway, J.: A Course in Functional Analysis. Springer, New York (1990)
Even, G., Naor, J., Rao, S., Schieber, B.: Divide-and-conquer approximation algorithms via spreading metrics. In: 36th Proc. on Foundations of Computer Science, pp. 62–71 (1995)
Feldman, M., Gilles, C.: An expository note on individual risk without aggregate uncertainty. J. Econ. Theory 35, 26–32 (1985)
Fishburn, P., Wright, P.: Bandwidth edge counts for linear arrangements of rectangular grids. J. Graph Theory 26(4), 195–202 (1997)
Garey, M.R., Graham, R.L., Johnson, D.S., Knuth, D.: Complexity results for bandwidth minimization. SIAM J. Appl. Math. 34, 477–495 (1978)
Gavril, F.: Some NP-complete problems on graphs. In: Proc. 11th Conf. on Information Sciences and Systems, Johns Hopkins University, pp. 91–95 (1977)
Harper, L.H.: Stabilization and the edgesum problem. Ars Combin. 4, 225–270 (1977)
Kargapolov, M., Merzljako, J.: Fundamentals of the Theory of Groups. Springer, New York (1979)
Kloks, T., Kratsch, D., Muller, H.: Bandwidth of chain graphs. Inf. Process. Lett. 68(6), 313–315 (1998)
Liu, J., Williams, K.: On bandwidth and edgesum for the composition of two graphs. Discrete Math. 143, 59–166 (1995)
Mahesh, R., Pandu, C., Srinivasan, A.: On finding the minimum bandwidth of interval graphs. Inf. Comput. 95, 218–224 (1991)
Monien, B., Sudborough, I.H.: Min-cut is NP-complete for Edge Weighted Trees. Lecture Notes in Computer Science, vol. 226. Springer, Berlin (1986)
Nakano, K., Chen, W., Masuzawa, T., Hagihara, K., Tokura, T.: Cut-width and bisection width of hypercube graph. IEICE Trans. J73-A, 856–862 (1990)
Raspaud, A., Sykora, O., Vrto, I.: Cutwidth of the de Bruijn graph. RAIRO. Inform. Theor. Appl. 29(6), 509–514 (1995)
Rolim, J., Sykora, O., Vrto, I.: Optimal Cutwidths of Meshes. Lecture Notes in Computer Science, vol. 1017, pp. 252–264. Springer, Berlin (1995)
Williams, K.: On bandwidth and edgesum for the tensor product of paths with complete bipartite graphs. Cong. Numer. 102, 183–190 (1994)
Yannakakis, M.: A polynomial algorithm for the min cut linear arrangement of trees. J. Assoc. Comput. Mach. 32, 950–989 (1985)
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Partially supported by the Lynn and William Frankel Center for Computer Sciences.
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Lipets, V. Bounds on Mincut for Cayley Graphs over Abelian Groups. Theory Comput Syst 45, 372–380 (2009). https://doi.org/10.1007/s00224-008-9105-2
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DOI: https://doi.org/10.1007/s00224-008-9105-2