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Title: | Continuous k-to-1 functions between complete graphs of even order |
Authors: | Dugdale, J. Keith Fiorini, Stanley Hilton, Anthony J.W. Gauci, John Baptist |
Keywords: | Complete graphs Functions, Continuous Graph theory -- Data processing Graphic methods -- Data processing |
Issue Date: | 2010 |
Publisher: | Elsevier BV. North-Holland |
Citation: | Dugdale, J. K., Fiorini, S., Hilton, A. J., & Gauci, J. B. (2010). Continuous k-to-1 functions between complete graphs of even order. Discrete Mathematics, 310(2), 330-346. |
Abstract: | A function between graphs is k-to-1 if each point in the co-domain has precisely k pre-images in the domain. Given two graphs, G and H, and an integer k ≥ 1, and considering G and H as subsets of R 3, there may or may not be a k-to-1 continuous function (i.e. a k-to-1 map in the usual topological sense) from G onto H. In this paper we review and complete the determination of whether there are finitely discontinuous, or just infinitely discontinuous k-to-1 functions between two intervals, each of which is one of the following: ]0, 1[, [0, 1[and [0, 1]. We also show that for k even and 1 ≤ r < 2s, (r, s) 6= (1, 1) and (r, s) 6= (3, 2), there is a k-to-1 map from K2r onto K2s if and only if k ≥ 2s. |
URI: | https://www.um.edu.mt/library/oar/handle/123456789/44848 |
Appears in Collections: | Scholarly Works - FacSciMat |
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Continuous_k_to_1_functions_between_complete_graphs_of_even_order.pdf | 835.48 kB | Adobe PDF | View/Open |
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