Abstract
For eachr-regular graphG, define a binary sequenceθ(G) = (θ 1,θ 2,...,θ r-1) byθ k = 0 ifG has ak-factor, andθ k = 1 otherwise. A binary sequenceε = (ε i |i = 1, 2,...,r − 1) is said to be realizable if there exists anr-regular graphG such thatθ(G) = ε. In this paper we characterize all binary sequences which are realizable.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Behzad, M., Chartrand, G., Lesniak-Foster, L.: Graphs and Digraphs. Boston: Wadsworth, Belmont, Calif. (1979)
Bollobás, B., Saito, A., Wormald, N.C.: Regular factors of regular graphs. J. Graph Theory9, 97–103 (1985)
Gallai, T.: On the factorization of graph. Acta Math. Acad. Sci. Hung.1, 133–153 (1950)
Kano, M., Saito, A.: [a, b]-factors of graphs. Discrete Math.47, 113–116 (1983)
Karterinis, P.: Some conditions for the existence off-factors. J. Graph Theory9, 513–521 (1985)
Peng, Y.H., Chen, C.C., Koh, K.M.: The factor-indices of completen-partite graphs. Research Report No. 297 Department of Mathematics, National University of Singapore (1987)
Petersen, J.: Die theorie der regulären graphen. Acta Math.15, 193–220 (1891)
Plesnik, J.: Remarks on regular factors of regular graphs. Czech. Math. J.24, 292–300 (1974)
Thomassen, C.: A remark on the factor theorems of Lovász and Tutte. J. Graph Theory8, 441–442 (1981)
Tutte, W.T.: The factors of graphs. Canada J. Math.4, 314–328 (1952)
Tutte, W.T.: The subgraph problem. Ann. Discrete Math.3, 289–295 (1978)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Peng, Y.H., Chen, C.C. & Koh, K.M. On the factor-thickness of regular graphs. Graphs and Combinatorics 5, 173–188 (1989). https://doi.org/10.1007/BF01788668
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01788668